Pub Date : 2025-12-31DOI: 10.1016/j.geomphys.2025.105748
Dongha Lee
We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient torsion, whose Hodge dual plays the role of an imaginary counterpart to mean curvature for surfaces in a Riemann-Cartan 3-manifold. We observe that this complex-valued geometric quantity interacts with a number of other geometric concepts including the Hopf differential and the Gauss map, which generalizes classical minimal surface theory.
{"title":"Complex-valued extension of mean curvature for surfaces in Riemann-Cartan geometry","authors":"Dongha Lee","doi":"10.1016/j.geomphys.2025.105748","DOIUrl":"10.1016/j.geomphys.2025.105748","url":null,"abstract":"<div><div>We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient torsion, whose Hodge dual plays the role of an imaginary counterpart to mean curvature for surfaces in a Riemann-Cartan 3-manifold. We observe that this complex-valued geometric quantity interacts with a number of other geometric concepts including the Hopf differential and the Gauss map, which generalizes classical minimal surface theory.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105748"},"PeriodicalIF":1.2,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-31DOI: 10.1016/j.geomphys.2025.105747
Keita Mori, Yasuhiro Wakabayashi
This note studies -opers arising from generalized hypergeometric differential equations in prime characteristic p. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the 2d TQFTs that compute the number of dormant -opers for primes .
{"title":"Generalized hypergeometric equations and 2d TQFT for dormant opers in characteristic ≤7","authors":"Keita Mori, Yasuhiro Wakabayashi","doi":"10.1016/j.geomphys.2025.105747","DOIUrl":"10.1016/j.geomphys.2025.105747","url":null,"abstract":"<div><div>This note studies <span><math><msub><mrow><mi>PGL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-opers arising from generalized hypergeometric differential equations in prime characteristic <em>p</em>. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the 2d TQFTs that compute the number of dormant <span><math><msub><mrow><mi>PGL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-opers for primes <span><math><mi>p</mi><mo>≤</mo><mn>7</mn></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105747"},"PeriodicalIF":1.2,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-30DOI: 10.1016/j.geomphys.2025.105743
Grigorios Giotopoulos , Hisham Sati , Urs Schreiber
We give a modernized and streamlined review, aimed at mathematical physicists, of the origin and nature of the super Lie-algebra known as the (“hidden”) M-algebra, which arises somewhat subtly in analysis of 11D supergravity. Following arguments that this (hidden) M-algebra serves in fact as the maximal super-exceptional tangent space for 11D supergravity, we particularly make explicit here its integration to a (super-Lie) group. This is equipped with a left-invariant extension of the “decomposed” M-theory 3-form, such that it constitutes the Kleinian space on which super-exceptional spacetimes are to be locally modeled as Cartan geometries.
As a simple but consequential application, we highlight how to describe lattice subgroups of the hidden M-group that allow to toroidially compactify also the “hidden” dimensions of a super-exceptional spacetime, akin to the familiar situation in topological T-duality.
In order to deal with subtleties in these constructions, we (i) provide a computer-checked re-derivation of the “decomposed” M-theory 3-form, and (ii) present a streamlined conception of super-Lie groups, that is both rigorous while still close to physics intuition and practice.
Thereby this article highlights modernized super-Lie theory along the example of the hidden M-algebra, with an eye towards laying foundations for super-exceptional geometry. Among new observations which we touch on along the way is the dimensional reduction of the hidden M-algebra to a “hidden IIA-algebra” which in [45] we have explained as the exceptional extension of the T-duality doubled super-spacetime.
{"title":"The hidden M-group","authors":"Grigorios Giotopoulos , Hisham Sati , Urs Schreiber","doi":"10.1016/j.geomphys.2025.105743","DOIUrl":"10.1016/j.geomphys.2025.105743","url":null,"abstract":"<div><div>We give a modernized and streamlined review, aimed at mathematical physicists, of the origin and nature of the super Lie-algebra known as the (“hidden”) <em>M-algebra</em>, which arises somewhat subtly in analysis of 11D supergravity. Following arguments that this (hidden) M-algebra serves in fact as the maximal super-exceptional tangent space for 11D supergravity, we particularly make explicit here its integration to a (super-Lie) <em>group</em>. This is equipped with a left-invariant extension of the “decomposed” M-theory 3-form, such that it constitutes the Kleinian space on which super-exceptional spacetimes are to be locally modeled as Cartan geometries.</div><div>As a simple but consequential application, we highlight how to describe lattice subgroups <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>k</mi><mo>≤</mo><mn>528</mn></mrow></msup></math></span> of the hidden M-group that allow to toroidially compactify also the “hidden” dimensions of a super-exceptional spacetime, akin to the familiar situation in topological T-duality.</div><div>In order to deal with subtleties in these constructions, we (i) provide a computer-checked re-derivation of the “decomposed” M-theory 3-form, and (ii) present a streamlined conception of super-Lie groups, that is both rigorous while still close to physics intuition and practice.</div><div>Thereby this article highlights modernized super-Lie theory along the example of the hidden M-algebra, with an eye towards laying foundations for super-exceptional geometry. Among new observations which we touch on along the way is the dimensional reduction of the hidden M-algebra to a “hidden IIA-algebra” which in <span><span>[45]</span></span> we have explained as the exceptional extension of the T-duality doubled super-spacetime.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105743"},"PeriodicalIF":1.2,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-30DOI: 10.1016/j.geomphys.2025.105746
Guolin An , Guangxiang Su
Let be a closed Riemannian manifold of dimension n, and let F be an integrable subbundle of TM. Let be the leafwise scalar curvature associated to . Let E be an oriented flat vector bundle. We show that if either TM or F is spin, and TM carries a metric satisfying that , the leafwise scalar curvature along F, is positive everywhere, then , where is the Hirzebruch -class of TM and is the Euler class of E. This extends the generalization of the Lichnerowicz vanishing theorem concerning the Euler class proved by Yu and Zhang to the case of foliations.
设（M,gTM）为n维的封闭黎曼流形，设F为TM的可积子束。设kF为与gF=gTM|F相关的叶向标量曲率。设E是一个有方向的平面向量束。我们证明了如果TM或F是自旋，并且TM携带一个度量gTM，满足沿F的叶向标量曲率kF处处为正，则< a - (TM)e(e),[M] > =0，其中a - (TM)是TM的Hirzebruch a -类，e(e)是e的欧拉类。这将Yu和Zhang证明的关于欧拉类的Lichnerowicz消失定理推广到叶分的情况。
{"title":"Positive scalar curvature on foliations and the Euler class","authors":"Guolin An , Guangxiang Su","doi":"10.1016/j.geomphys.2025.105746","DOIUrl":"10.1016/j.geomphys.2025.105746","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>M</mi><mo>,</mo><msup><mrow><mi>g</mi></mrow><mrow><mi>T</mi><mi>M</mi></mrow></msup><mo>)</mo></math></span> be a closed Riemannian manifold of dimension <em>n</em>, and let <em>F</em> be an integrable subbundle of <em>TM</em>. Let <span><math><msup><mrow><mi>k</mi></mrow><mrow><mi>F</mi></mrow></msup></math></span> be the leafwise scalar curvature associated to <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>F</mi></mrow></msup><mo>=</mo><msup><mrow><mi>g</mi></mrow><mrow><mi>T</mi><mi>M</mi></mrow></msup><msub><mrow><mo>|</mo></mrow><mrow><mi>F</mi></mrow></msub></math></span>. Let <em>E</em> be an oriented flat vector bundle. We show that if either <em>TM</em> or <em>F</em> is spin, and <em>TM</em> carries a metric <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>T</mi><mi>M</mi></mrow></msup></math></span> satisfying that <span><math><msup><mrow><mi>k</mi></mrow><mrow><mi>F</mi></mrow></msup></math></span>, the leafwise scalar curvature along <em>F</em>, is positive everywhere, then <span><math><mo>〈</mo><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>T</mi><mi>M</mi><mo>)</mo><mi>e</mi><mo>(</mo><mi>E</mi><mo>)</mo><mo>,</mo><mo>[</mo><mi>M</mi><mo>]</mo><mo>〉</mo><mo>=</mo><mn>0</mn></math></span>, where <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>T</mi><mi>M</mi><mo>)</mo></math></span> is the Hirzebruch <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>-class of <em>TM</em> and <span><math><mi>e</mi><mo>(</mo><mi>E</mi><mo>)</mo></math></span> is the Euler class of <em>E</em>. This extends the generalization of the Lichnerowicz vanishing theorem concerning the Euler class proved by Yu and Zhang to the case of foliations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105746"},"PeriodicalIF":1.2,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-30DOI: 10.1016/j.geomphys.2025.105749
A.V. Smilga
It was recently found that a necessary and sufficient condition for a Kähler manifold to be hyperkähler reads(1) where is a complex metric, is a symplectic matrix and C is a positive constant.
In this note, we give a simple explicit proof of this fact.
{"title":"On the multidimensional heavenly equation","authors":"A.V. Smilga","doi":"10.1016/j.geomphys.2025.105749","DOIUrl":"10.1016/j.geomphys.2025.105749","url":null,"abstract":"<div><div>It was recently found that a necessary and sufficient condition for a Kähler manifold to be hyperkähler reads<span><span><span>(1)</span><span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi><mover><mrow><mi>k</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><msub><mrow><mi>h</mi></mrow><mrow><mi>j</mi><mover><mrow><mi>l</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub><msup><mrow><mi>Ω</mi></mrow><mrow><mover><mrow><mi>k</mi></mrow><mrow><mo>¯</mo></mrow></mover><mover><mrow><mi>l</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msup><mspace></mspace><mo>=</mo><mspace></mspace><mi>C</mi><msub><mrow><mi>Ω</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>,</mo></mrow></math></span></span></span> where <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi><mover><mrow><mi>k</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></msub></math></span> is a complex metric, <span><math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span> is a symplectic matrix and <em>C</em> is a positive constant.</div><div>In this note, we give a simple explicit proof of this fact.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105749"},"PeriodicalIF":1.2,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.geomphys.2025.105745
Mark D. Hamilton , Yael Karshon , Takahiko Yoshida
We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann–Roch number coincides with its number of Bohr–Sommerfeld fibres. This can be viewed as an instance of the “independence of polarization” phenomenon of geometric quantization. The base space for such a fibration acquires a so-called integral-integral affine structure. The proof uses the following simple fact, whose proof is trickier than we expected: on a compact integral-integral affine manifold, the total volume is equal to the number of integer points.
{"title":"Integral-integral affine geometry, geometric quantization, and Riemann–Roch","authors":"Mark D. Hamilton , Yael Karshon , Takahiko Yoshida","doi":"10.1016/j.geomphys.2025.105745","DOIUrl":"10.1016/j.geomphys.2025.105745","url":null,"abstract":"<div><div>We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann–Roch number coincides with its number of Bohr–Sommerfeld fibres. This can be viewed as an instance of the “independence of polarization” phenomenon of geometric quantization. The base space for such a fibration acquires a so-called integral-integral affine structure. The proof uses the following simple fact, whose proof is trickier than we expected: on a compact integral-integral affine manifold, the total volume is equal to the number of integer points.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105745"},"PeriodicalIF":1.2,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.geomphys.2025.105742
Rutwig Campoamor-Stursberg , Oscar Carballal , Francisco J. Herranz
We propose an adaptation of the notion of scaling symmetries for the case of Lie–Hamilton systems, allowing their subsequent reduction to contact Lie systems. As an illustration of the procedure, time-dependent frequency oscillators and time-dependent thermodynamic systems are analyzed from this point of view. The formalism provides a novel method for constructing contact Lie systems on the three-dimensional sphere, derived from recently established Lie–Hamilton systems arising from the fundamental four-dimensional representation of the symplectic Lie algebra . It is shown that these systems are a particular case of a larger hierarchy of contact Lie systems on a special class of three-dimensional homogeneous spaces, namely the Cayley–Klein spaces. These include Riemannian spaces (sphere, hyperbolic and Euclidean spaces), pseudo-Riemannian spaces (anti-de Sitter, de Sitter and Minkowski spacetimes), as well as Newtonian or non-relativistic spacetimes. Under certain topological conditions, some of these systems retrieve well-known two-dimensional Lie–Hamilton systems through a curvature-dependent reduction.
{"title":"Contact Lie systems on Riemannian and Lorentzian spaces: From scaling symmetries to curvature-dependent reductions","authors":"Rutwig Campoamor-Stursberg , Oscar Carballal , Francisco J. Herranz","doi":"10.1016/j.geomphys.2025.105742","DOIUrl":"10.1016/j.geomphys.2025.105742","url":null,"abstract":"<div><div>We propose an adaptation of the notion of scaling symmetries for the case of Lie–Hamilton systems, allowing their subsequent reduction to contact Lie systems. As an illustration of the procedure, time-dependent frequency oscillators and time-dependent thermodynamic systems are analyzed from this point of view. The formalism provides a novel method for constructing contact Lie systems on the three-dimensional sphere, derived from recently established Lie–Hamilton systems arising from the fundamental four-dimensional representation of the symplectic Lie algebra <span><math><mi>s</mi><mi>p</mi><mo>(</mo><mn>4</mn><mo>,</mo><mi>R</mi><mo>)</mo></math></span>. It is shown that these systems are a particular case of a larger hierarchy of contact Lie systems on a special class of three-dimensional homogeneous spaces, namely the Cayley–Klein spaces. These include Riemannian spaces (sphere, hyperbolic and Euclidean spaces), pseudo-Riemannian spaces (anti-de Sitter, de Sitter and Minkowski spacetimes), as well as Newtonian or non-relativistic spacetimes. Under certain topological conditions, some of these systems retrieve well-known two-dimensional Lie–Hamilton systems through a curvature-dependent reduction.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105742"},"PeriodicalIF":1.2,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-29DOI: 10.1016/j.geomphys.2025.105744
Kiyoon Eum
In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized Kähler manifold. We show that the coefficients of the expansion are given by geometric functionals on Kähler metrics satisfying the cocycle identity, whose first variations can be expressed through the TYZ expansion coefficients of the Bergman kernel. In particular, these functionals naturally generalize the Mabuchi functional in Kähler geometry and the Liouville functional on Riemann surfaces. We further show that Futaki-type holomorphic invariants obstruct the existence of critical points of these geometric functionals, extending Lu's formula. We also verify that certain formulas remain valid up to the third coefficient without assuming polarization. Finally, we discuss the relation of our results to the quantum Hall effect (QHE), where the determinantal point process provides a microscopic model. In particular, we recover the higher-dimensional effective Chern-Simons actions derived in the physics literature and confirm a conjecture of Klevtsov on the form of the partition function asymptotics.
{"title":"Partition functions of determinantal point processes on polarized Kähler manifolds","authors":"Kiyoon Eum","doi":"10.1016/j.geomphys.2025.105744","DOIUrl":"10.1016/j.geomphys.2025.105744","url":null,"abstract":"<div><div>In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized Kähler manifold. We show that the coefficients of the expansion are given by geometric functionals on Kähler metrics satisfying the cocycle identity, whose first variations can be expressed through the TYZ expansion coefficients of the Bergman kernel. In particular, these functionals naturally generalize the Mabuchi functional in Kähler geometry and the Liouville functional on Riemann surfaces. We further show that Futaki-type holomorphic invariants obstruct the existence of critical points of these geometric functionals, extending Lu's formula. We also verify that certain formulas remain valid up to the third coefficient without assuming polarization. Finally, we discuss the relation of our results to the quantum Hall effect (QHE), where the determinantal point process provides a microscopic model. In particular, we recover the higher-dimensional effective Chern-Simons actions derived in the physics literature and confirm a conjecture of Klevtsov on the form of the partition function asymptotics.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105744"},"PeriodicalIF":1.2,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1016/j.geomphys.2025.105741
Vladimir Rovenski , Milan Zlatanović
Linear connections with torsion are important in the study of generalized Riemannian manifolds , where the symmetric part g of G is a non-degenerate -tensor and F is the skew-symmetric part. Some space-time models in theoretical physics are based on , where F is defined using an almost complex or almost contact metric structure.
In the paper, we first study more general models, where F has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric structures. We consider generalized metric connections (i.e., linear connections preserving G) with totally skew-symmetric torsion -tensor. For rank and non-conformal tensor , where A is a skew-symmetric -tensor adjoint to F, we apply weak almost Hermitian structures to fundamental results (by the second author and S. Ivanov) on generalized Riemannian manifolds and prove that the manifold is a weighted product of several nearly Kähler manifolds corresponding to eigen-distributions of . For rank we apply weak f-structures and obtain splitting results for generalized Riemannian manifolds.
在广义黎曼流形（M，G= G +F）的研究中，具有扭转的线性连接是重要的，其中G的对称部分G是一个非简并（0,2）张量，F是偏对称部分。理论物理中的一些时空模型基于（M，G= G +F），其中F是使用几乎复杂或几乎接触的度量结构来定义的。在本文中，我们首先研究了更一般的模型，其中F具有常数秩，并且基于弱度量结构（由第一作者和R. Wolak引入），它推广了几乎复杂和几乎接触的度量结构。我们考虑具有完全偏对称扭转（0,3）张量的广义度量连接（即保持G的线性连接）。对于秩(F)=dim (M)和非共形张量A2，其中A是F的一个偏对称(1,1)-张量，我们将弱几乎埃尔米结构应用于第二作者和S. Ivanov关于广义黎曼流形的基本结果，并证明了该流形是与A2的特征分布相对应的几个近似Kähler流形的加权积。对于rank(F)<dim (M)，我们应用弱F结构，得到广义黎曼流形的分裂结果。
{"title":"Weak metric structures on generalized Riemannian manifolds","authors":"Vladimir Rovenski , Milan Zlatanović","doi":"10.1016/j.geomphys.2025.105741","DOIUrl":"10.1016/j.geomphys.2025.105741","url":null,"abstract":"<div><div>Linear connections with torsion are important in the study of generalized Riemannian manifolds <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>G</mi><mo>=</mo><mi>g</mi><mo>+</mo><mi>F</mi><mo>)</mo></math></span>, where the symmetric part <em>g</em> of <em>G</em> is a non-degenerate <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>-tensor and <em>F</em> is the skew-symmetric part. Some space-time models in theoretical physics are based on <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>G</mi><mo>=</mo><mi>g</mi><mo>+</mo><mi>F</mi><mo>)</mo></math></span>, where <em>F</em> is defined using an almost complex or almost contact metric structure.</div><div>In the paper, we first study more general models, where <em>F</em> has constant rank and is based on weak metric structures (introduced by the first author and R. Wolak), which generalize almost complex and almost contact metric structures. We consider generalized metric connections (i.e., linear connections preserving <em>G</em>) with totally skew-symmetric torsion <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span>-tensor. For rank<span><math><mo>(</mo><mi>F</mi><mo>)</mo><mo>=</mo><mi>dim</mi><mo></mo><mi>M</mi></math></span> and non-conformal tensor <span><math><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <em>A</em> is a skew-symmetric <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-tensor adjoint to <em>F</em>, we apply weak almost Hermitian structures to fundamental results (by the second author and S. Ivanov) on generalized Riemannian manifolds and prove that the manifold is a weighted product of several nearly Kähler manifolds corresponding to eigen-distributions of <span><math><msup><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. For rank<span><math><mo>(</mo><mi>F</mi><mo>)</mo><mo><</mo><mi>dim</mi><mo></mo><mi>M</mi></math></span> we apply weak <em>f</em>-structures and obtain splitting results for generalized Riemannian manifolds.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105741"},"PeriodicalIF":1.2,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-17DOI: 10.1016/j.geomphys.2025.105740
Tung Tran
We present twistor BV actions that encompass many classically consistent bosonic holomorphic twistorial higher-spin theories with vanishing cosmological constant. Upon quantization, these actions are shown to be quantum consistent, i.e. no gauge anomaly, for some subclasses of twistorial higher-spin theories. Anomaly-free twistorial theories can be identified through an index theorem, which is a higher-spin extension of the Hirzebruch-Riemann-Roch index theorem. We also discuss the anomaly cancellation mechanisms on twistor space to render anomalous theories quantum consistent at one loop.
{"title":"Anomaly-free twistorial higher-spin theories","authors":"Tung Tran","doi":"10.1016/j.geomphys.2025.105740","DOIUrl":"10.1016/j.geomphys.2025.105740","url":null,"abstract":"<div><div>We present twistor BV actions that encompass many classically consistent bosonic holomorphic twistorial higher-spin theories with vanishing cosmological constant. Upon quantization, these actions are shown to be quantum consistent, i.e. no gauge anomaly, for some subclasses of twistorial higher-spin theories. Anomaly-free twistorial theories can be identified through an index theorem, which is a higher-spin extension of the Hirzebruch-Riemann-Roch index theorem. We also discuss the anomaly cancellation mechanisms on twistor space to render anomalous theories quantum consistent at one loop.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105740"},"PeriodicalIF":1.2,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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