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Differential Geometry and its Applications最新文献

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Darboux-Lie derivatives Darboux-Lie衍生品
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-10-16 DOI: 10.1016/j.difgeo.2025.102305
Antonio De Nicola , Ivan Yudin
{"title":"Darboux-Lie derivatives","authors":"Antonio De Nicola ,&nbsp;Ivan Yudin","doi":"10.1016/j.difgeo.2025.102305","DOIUrl":"10.1016/j.difgeo.2025.102305","url":null,"abstract":"<div><div>We introduce the Darboux-Lie derivative along a vector field of fiber bundle maps from natural bundles to associated fiber bundles and study its properties.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102305"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The completeness problem on the pseudo-homothetic Lie group 伪齐调李群上的完备性问题
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-09 DOI: 10.1016/j.difgeo.2025.102288
Salah Chaib , Ana Cristina Ferreira , Abdelghani Zeghib
{"title":"The completeness problem on the pseudo-homothetic Lie group","authors":"Salah Chaib ,&nbsp;Ana Cristina Ferreira ,&nbsp;Abdelghani Zeghib","doi":"10.1016/j.difgeo.2025.102288","DOIUrl":"10.1016/j.difgeo.2025.102288","url":null,"abstract":"<div><div>Let us call pseudo-homothetic group the non-unimodular 3-dimensional Lie group that is the semi-direct product of <span><math><mi>R</mi></math></span> acting non-semisimply on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. In this article, we solve the geodesic completeness problem on this Lie group. In particular, we exhibit a family of complete metrics such that all geodesics have bounded velocity. As an application, we show that the set of complete metrics is not closed.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102288"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Euler-Poincaré reduction for central extension 中心扩展的随机euler - poincarcarr约简
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-11 DOI: 10.1016/j.difgeo.2025.102290
Ali Suri
{"title":"Stochastic Euler-Poincaré reduction for central extension","authors":"Ali Suri","doi":"10.1016/j.difgeo.2025.102290","DOIUrl":"10.1016/j.difgeo.2025.102290","url":null,"abstract":"<div><div>This paper explores the application of central extensions of Lie groups and Lie algebras to derive the viscous quasi-geostrophic (QGS) equations, with and without Rayleigh friction term, on the torus as critical points of a stochastic Lagrangian. We begin by introducing central extensions and proving the integrability of the Roger Lie algebra cocycle <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>, which is used to model the QGS on the torus. Incorporating stochastic perturbations, we formulate two specific semi-martingales on the central extension and study the stochastic Euler-Poincaré reduction. Specifically, we add stochastic perturbations to the <span><math><mi>g</mi></math></span> part of the extended Lie algebra <span><math><mover><mrow><mi>g</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>=</mo><mi>g</mi><msub><mrow><mo>⋊</mo></mrow><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>α</mi></mrow></msub></mrow></msub><mi>R</mi></math></span> and prove that the resulting critical points of the stochastic right-invariant Lagrangian solve the viscous QGS equation, with and without Rayleigh friction term.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102290"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A class of new complete affine maximal type hypersurfaces 一类新的完全仿射极大型超曲面
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-11-10 DOI: 10.1016/j.difgeo.2025.102308
Yalin Sun, Ruiwei Xu
{"title":"A class of new complete affine maximal type hypersurfaces","authors":"Yalin Sun,&nbsp;Ruiwei Xu","doi":"10.1016/j.difgeo.2025.102308","DOIUrl":"10.1016/j.difgeo.2025.102308","url":null,"abstract":"<div><div>In this paper we classify a kind of special Calabi hypersurfaces with negative constant sectional curvature in Calabi affine geometry. Meanwhile, we find a class of new Euclidean complete and Calabi complete affine hypersurfaces, which satisfy the affine maximal type equation and the Abreu equation with negative constant scalar curvatures.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102308"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximal antipodal sets of compact classical symmetric spaces and their cardinalities. II 紧经典对称空间的极大对映集及其基数。2
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-10-14 DOI: 10.1016/j.difgeo.2025.102302
Makiko Sumi Tanaka , Hiroyuki Tasaki
{"title":"Maximal antipodal sets of compact classical symmetric spaces and their cardinalities. II","authors":"Makiko Sumi Tanaka ,&nbsp;Hiroyuki Tasaki","doi":"10.1016/j.difgeo.2025.102302","DOIUrl":"10.1016/j.difgeo.2025.102302","url":null,"abstract":"<div><div>In the authors' article in 2020 we classified and explicitly described maximal antipodal sets of Grassmann manifolds, compact symmetric spaces <span><math><mi>C</mi><mi>I</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>, <span><math><mi>D</mi><mi>I</mi><mi>I</mi><mi>I</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and their quotient spaces. In this article we show similar results for compact symmetric spaces <span><math><mi>U</mi><mi>I</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><mi>U</mi><mi>I</mi><mi>I</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and their quotient spaces by using realizations of these as polars in disconnected compact Lie groups.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102302"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability and rigidity of 3-Lie algebra morphisms 3-Lie代数态射的稳定性和刚性
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-02 DOI: 10.1016/j.difgeo.2025.102278
Jun Jiang, Yunhe Sheng, Geyi Sun
{"title":"Stability and rigidity of 3-Lie algebra morphisms","authors":"Jun Jiang,&nbsp;Yunhe Sheng,&nbsp;Geyi Sun","doi":"10.1016/j.difgeo.2025.102278","DOIUrl":"10.1016/j.difgeo.2025.102278","url":null,"abstract":"<div><div>In this paper, first we use the higher derived brackets to construct an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra, whose Maurer-Cartan elements are 3-Lie algebra morphisms. Using the differential in the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra that govern deformations of the morphism, we give the cohomology of a 3-Lie algebra morphism. Then we study the rigidity and stability of 3-Lie algebra morphisms using the established cohomology theory. In particular, we show that if the first cohomology group is trivial, then the morphism is rigid; if the second cohomology group is trivial, then the morphism is stable. Finally, we study the stability of 3-Lie subalgebras similarly.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102278"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal and harmonic vector fields on three-dimensional C12-manifolds 三维c12流形上的极小和调和向量场
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-11 DOI: 10.1016/j.difgeo.2025.102289
Gherici Beldjilali
{"title":"Minimal and harmonic vector fields on three-dimensional C12-manifolds","authors":"Gherici Beldjilali","doi":"10.1016/j.difgeo.2025.102289","DOIUrl":"10.1016/j.difgeo.2025.102289","url":null,"abstract":"<div><div>In this paper, we obtain some necessary and sufficient conditions for a vector field on a 3-dimensional <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>-manifold to be minimal or harmonic. We construct some examples to illustrate main results.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102289"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalised spinr structures on homogeneous spaces 齐次空间上的广义旋旋结构
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-12 DOI: 10.1016/j.difgeo.2025.102291
Diego Artacho, Marie-Amélie Lawn
{"title":"Generalised spinr structures on homogeneous spaces","authors":"Diego Artacho,&nbsp;Marie-Amélie Lawn","doi":"10.1016/j.difgeo.2025.102291","DOIUrl":"10.1016/j.difgeo.2025.102291","url":null,"abstract":"<div><div>Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of <em>G</em>-invariance of spin<sup><em>r</em></sup> structures on a manifold <em>M</em> equipped with an action of a Lie group <em>G</em>. For the case when <em>M</em> is a homogeneous <em>G</em>-space, we prove a classification result of these invariant structures in terms of the isotropy representation. As an example, we study the invariant spin<sup><em>r</em></sup> structures for all the homogeneous realisations of the spheres.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102291"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vector fields and derivations on differentiable stacks 可微堆栈上的向量场和导数
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-16 DOI: 10.1016/j.difgeo.2025.102292
Juan Sebastián Herrera-Carmona , Cristian Ortiz , James Waldron
{"title":"Vector fields and derivations on differentiable stacks","authors":"Juan Sebastián Herrera-Carmona ,&nbsp;Cristian Ortiz ,&nbsp;James Waldron","doi":"10.1016/j.difgeo.2025.102292","DOIUrl":"10.1016/j.difgeo.2025.102292","url":null,"abstract":"<div><div>We introduce and study module structures on both the dgla of multiplicative vector fields and the graded algebra of functions on Lie groupoids. We show that there is an associated structure of a graded Lie-Rinehart algebra on the vector fields of a differentiable stack over its smooth functions that is Morita invariant in an appropriate sense. Furthermore, we show that associated Van-Est type maps are compatible with those module structures. We also present several examples.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102292"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized weakly-Weyl Finsler metrics: A generalized approach to Sakaguchi's theorem 广义弱weyl - Finsler度量：Sakaguchi定理的广义方法
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-12-01 Epub Date: 2025-09-19 DOI: 10.1016/j.difgeo.2025.102297
Nasrin Sadeghzadeh, Meshkat Yavari
{"title":"Generalized weakly-Weyl Finsler metrics: A generalized approach to Sakaguchi's theorem","authors":"Nasrin Sadeghzadeh,&nbsp;Meshkat Yavari","doi":"10.1016/j.difgeo.2025.102297","DOIUrl":"10.1016/j.difgeo.2025.102297","url":null,"abstract":"<div><div>The development of projective invariant Weyl metrics in this paper offers a fresh perspective, as we establish the characteristics of both weakly-Weyl and generalized weakly-Weyl Finsler metrics. We thoroughly examine the connections between these metrics and various projective invariants, highlighting their significance in the context of generalized Sakaguchi's Theorem, which states that every Finsler metric of scalar flag curvature is a GDW-metric. Additionally, we introduce several illustrative examples pertaining to this new class of projective invariant Finsler metrics. Specifically, we explore the category of weakly-Weyl spherically symmetric Finsler metrics in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Importantly, we demonstrate that the two classes weakly-Weyl and <em>W</em>-quadratic spherically symmetric Finsler metrics in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> are equivalent.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102297"},"PeriodicalIF":0.7,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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