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}
Pub Date : 2025-12-17DOI: 10.1016/j.geomphys.2025.105739
Yujie Li, Nan Liu
This paper systematically studies the discrete modified Korteweg–de Vries (mKdV) equation with arbitrary-order poles based on the Riemann–Hilbert (RH) approach. Firstly, in the direct scattering problem, we present a complete analysis for the analyticity, asymptotic behaviors, and symmetries of the Jost solutions and scattering data. In particular, a detailed analysis of the discrete spectrum associated with 2N pairs arbitrary-order poles is provided. Secondly, in the inverse scattering problem, we construct a canonical matrix RH problem with residue conditions characterized at these 2N pairs of poles. By solving the RH problem, we derive the reconstruction formula for the solution of the discrete mKdV equation. Finally, in the reflectionless case, the inverse problem can be reduced to a set of linear algebraic equations, which allows us to provide an explicit parametric representation of higher-order soliton solutions.
{"title":"Riemann–Hilbert approach for discrete mKdV equation with arbitrary-order poles","authors":"Yujie Li, Nan Liu","doi":"10.1016/j.geomphys.2025.105739","DOIUrl":"10.1016/j.geomphys.2025.105739","url":null,"abstract":"<div><div>This paper systematically studies the discrete modified Korteweg–de Vries (mKdV) equation with arbitrary-order poles based on the Riemann–Hilbert (RH) approach. Firstly, in the direct scattering problem, we present a complete analysis for the analyticity, asymptotic behaviors, and symmetries of the Jost solutions and scattering data. In particular, a detailed analysis of the discrete spectrum associated with 2<em>N</em> pairs arbitrary-order poles is provided. Secondly, in the inverse scattering problem, we construct a canonical <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrix RH problem with residue conditions characterized at these 2<em>N</em> pairs of poles. By solving the RH problem, we derive the reconstruction formula for the solution of the discrete mKdV equation. Finally, in the reflectionless case, the inverse problem can be reduced to a set of linear algebraic equations, which allows us to provide an explicit parametric representation of higher-order soliton solutions.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105739"},"PeriodicalIF":1.2,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841321","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 : 2025-12-08DOI: 10.1016/j.geomphys.2025.105738
Manuel Ladra , Pilar Páez-Guillán
We prove an eight-term exact sequence in the homology of Lie superalgebras. We use the technique of the non-abelian tensor product to prove Schur- and Baer-type theorems for Lie superalgebras.
{"title":"The non-abelian tensor product of Lie superalgebras and Schur- and Baer-type theorems","authors":"Manuel Ladra , Pilar Páez-Guillán","doi":"10.1016/j.geomphys.2025.105738","DOIUrl":"10.1016/j.geomphys.2025.105738","url":null,"abstract":"<div><div>We prove an eight-term exact sequence in the homology of Lie superalgebras. We use the technique of the non-abelian tensor product to prove Schur- and Baer-type theorems for Lie superalgebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105738"},"PeriodicalIF":1.2,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747575","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 : 2025-12-03DOI: 10.1016/j.geomphys.2025.105723
Andrey Losev , Dmitrii Sheptunov , Xin Geng
One of the approaches to quantum gravity is to formulate it in terms of de Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue in general relativity is the action of diffeomorphisms of space-time on fields. In this paper, we induce the action of diffeomorphisms on cochains by homotopy transfer (or, equivalently, BV integral) that leads to an action. We explicitly compute this action for the space-time, being an interval and a circle.
{"title":"On induced L∞ action of diffeomorphisms on cochains","authors":"Andrey Losev , Dmitrii Sheptunov , Xin Geng","doi":"10.1016/j.geomphys.2025.105723","DOIUrl":"10.1016/j.geomphys.2025.105723","url":null,"abstract":"<div><div>One of the approaches to quantum gravity is to formulate it in terms of de Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue in general relativity is the action of diffeomorphisms of space-time on fields. In this paper, we induce the action of diffeomorphisms on cochains by homotopy transfer (or, equivalently, BV integral) that leads to an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> action. We explicitly compute this action for the space-time, being an interval and a circle.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"221 ","pages":"Article 105723"},"PeriodicalIF":1.2,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145697786","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 : 2025-12-01DOI: 10.1016/j.geomphys.2025.105721
Ron Donagi , Nadia Ott
{"title":"Supermoduli space with Ramond punctures is not projected","authors":"Ron Donagi , Nadia Ott","doi":"10.1016/j.geomphys.2025.105721","DOIUrl":"10.1016/j.geomphys.2025.105721","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105721"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693740","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 : 2025-12-01DOI: 10.1016/j.geomphys.2025.105730
Dongmei Zhang , Fangyang Zheng
In 1976, Milnor classified all Lie groups admitting a flat left-invariant metric. They form a special type of unimodular 2-step solvable groups. Considering Lie groups with Hermitian structure, namely, a left-invariant complex structure and a compatible left-invariant metric, in 2006, Barberis-Dotti-Fino obtained among other things full classification of all Lie groups with Hermitian structure that are Kähler and flat. In this note, we examine Lie groups with a Hermitian structure that are flat, and show that they actually must be Kähler, or equivalently speaking, a flat Hermitian Lie algebra is always Kähler. In the proofs we utilized analysis on the Hermitian geometry of 2-step solvable Lie groups developed by Freibert-Swann and by Chen and the second named author.
{"title":"Flat Hermitian Lie algebras are Kähler","authors":"Dongmei Zhang , Fangyang Zheng","doi":"10.1016/j.geomphys.2025.105730","DOIUrl":"10.1016/j.geomphys.2025.105730","url":null,"abstract":"<div><div>In 1976, Milnor classified all Lie groups admitting a flat left-invariant metric. They form a special type of unimodular 2-step solvable groups. Considering Lie groups with Hermitian structure, namely, a left-invariant complex structure and a compatible left-invariant metric, in 2006, Barberis-Dotti-Fino obtained among other things full classification of all Lie groups with Hermitian structure that are Kähler and flat. In this note, we examine Lie groups with a Hermitian structure that are flat, and show that they actually must be Kähler, or equivalently speaking, a flat Hermitian Lie algebra is always Kähler. In the proofs we utilized analysis on the Hermitian geometry of 2-step solvable Lie groups developed by Freibert-Swann and by Chen and the second named author.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105730"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693744","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 : 2025-12-01DOI: 10.1016/j.geomphys.2025.105722
Oleg I. Morozov
We combine the construction of the canonical conservation law and the nonlocal cosymmetry to derive a collection of nonlocal conservation laws for the two-dimensional Euler equation in vorticity form. For computational convenience and simplicity of presentation of the results we perform a complex rotation of the independent variables.
{"title":"Nonlocal conservation laws for the two-dimensional Euler equation in vorticity form","authors":"Oleg I. Morozov","doi":"10.1016/j.geomphys.2025.105722","DOIUrl":"10.1016/j.geomphys.2025.105722","url":null,"abstract":"<div><div>We combine the construction of the canonical conservation law and the nonlocal cosymmetry to derive a collection of nonlocal conservation laws for the two-dimensional Euler equation in vorticity form. For computational convenience and simplicity of presentation of the results we perform a complex rotation of the independent variables.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105722"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693743","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 : 2025-11-24DOI: 10.1016/j.geomphys.2025.105719
Soumalya Joardar, Atibur Rahaman
This is a continuation of the work done by the authors in [5]. In [5], an almost complex structure on finitely many points from bidirected polygon was introduced. In this paper we study a Kähler structure on finite set of points. In particular, we study the edge Laplacian of a graph twisted by the Kähler structure introduced in this paper. We also discuss a metric aspect from a twisted holomorphic Dolbeault–Dirac spectral triple and show that the points have a finite diameter with respect to the Connes' distance.
{"title":"Twisted edge Laplacians on finite graphs from a Kähler structure","authors":"Soumalya Joardar, Atibur Rahaman","doi":"10.1016/j.geomphys.2025.105719","DOIUrl":"10.1016/j.geomphys.2025.105719","url":null,"abstract":"<div><div>This is a continuation of the work done by the authors in <span><span>[5]</span></span>. In <span><span>[5]</span></span>, an almost complex structure on finitely many points from bidirected polygon was introduced. In this paper we study a Kähler structure on finite set of points. In particular, we study the edge Laplacian of a graph twisted by the Kähler structure introduced in this paper. We also discuss a metric aspect from a twisted holomorphic Dolbeault–Dirac spectral triple and show that the points have a finite diameter with respect to the Connes' distance.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105719"},"PeriodicalIF":1.2,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624554","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 : 2025-11-24DOI: 10.1016/j.geomphys.2025.105720
G.B. Shabat , V.V. Sokolov , A.V. Tsiganov
We consider Novikov equations for commutative ring generated by differential operators of orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve of genus 2 for the Novikov equations.
{"title":"Novikov equations for commuting differential operators of orders 3,4,5","authors":"G.B. Shabat , V.V. Sokolov , A.V. Tsiganov","doi":"10.1016/j.geomphys.2025.105720","DOIUrl":"10.1016/j.geomphys.2025.105720","url":null,"abstract":"<div><div>We consider Novikov equations for commutative ring generated by differential operators of orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve of genus 2 for the Novikov equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105720"},"PeriodicalIF":1.2,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624551","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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