{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105772"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147077758","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}
{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105762"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147077770","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}
{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105743"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147077775","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}
{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"224 ","pages":"Article 105796"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147267094","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}
{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"224 ","pages":"Article 105797"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147267096","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.2025.105748
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}
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