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Differential Geometry and its Applications最新文献

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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 : 2025-09-11 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":"2025-09-11","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
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 : 2025-09-11 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":"2025-09-11","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
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 : 2025-09-09 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":"2025-09-09","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
Minimal hypersurfaces in S5 with constant scalar curvature and zero Gauss curvature 具有常标量曲率和零高斯曲率的S5极小超曲面
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-09 DOI: 10.1016/j.difgeo.2025.102279
Qing Cui
{"title":"Minimal hypersurfaces in S5 with constant scalar curvature and zero Gauss curvature","authors":"Qing Cui","doi":"10.1016/j.difgeo.2025.102279","DOIUrl":"10.1016/j.difgeo.2025.102279","url":null,"abstract":"<div><div>We show that a closed minimal hypersurface in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span> with constant scalar curvature and zero Gauss curvature is totally geodesic, which gives a support to strong version of Chern conjecture.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"101 ","pages":"Article 102279"},"PeriodicalIF":0.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020439","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 : 2025-09-02 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":"2025-09-02","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
Hamilton Lie algebroids over Dirac structures and sigma models 狄拉克结构和模型上的汉密尔顿李代数
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-08-25 DOI: 10.1016/j.difgeo.2025.102277
Noriaki Ikeda
{"title":"Hamilton Lie algebroids over Dirac structures and sigma models","authors":"Noriaki Ikeda","doi":"10.1016/j.difgeo.2025.102277","DOIUrl":"10.1016/j.difgeo.2025.102277","url":null,"abstract":"<div><div>We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poisson manifold. A Hamiltonian Lie algebroid and a momentum section generalize a Hamiltonian <em>G</em>-space and a momentum map over a symplectic manifold. We prove some properties of this new Hamiltonian Lie algebroid and construct a mechanics based on this structure as an application. These new mechanics are called the gauged Poisson sigma model and the gauged Dirac sigma model.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102277"},"PeriodicalIF":0.7,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893640","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
On the structure of homogeneous local Poisson brackets 齐次局部泊松括号的结构
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-08-25 DOI: 10.1016/j.difgeo.2025.102276
Guido Carlet , Matteo Casati
{"title":"On the structure of homogeneous local Poisson brackets","authors":"Guido Carlet ,&nbsp;Matteo Casati","doi":"10.1016/j.difgeo.2025.102276","DOIUrl":"10.1016/j.difgeo.2025.102276","url":null,"abstract":"<div><div>We consider an arbitrary Dubrovin-Novikov bracket of degree <em>k</em>, namely a homogeneous degree <em>k</em> local Poisson bracket on the loop space of a smooth manifold <em>M</em> of dimension <em>n</em>, and show that <em>k</em> connections, defined by explicit linear combinations with constant coefficients of the standard connections associated with the Poisson bracket, are flat.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102276"},"PeriodicalIF":0.7,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893641","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 Simons type condition for instability of F-Yang-Mills connections F-Yang-Mills连接不稳定的Simons型条件
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-08-20 DOI: 10.1016/j.difgeo.2025.102275
Kurando Baba , Kazuto Shintani
{"title":"A Simons type condition for instability of F-Yang-Mills connections","authors":"Kurando Baba ,&nbsp;Kazuto Shintani","doi":"10.1016/j.difgeo.2025.102275","DOIUrl":"10.1016/j.difgeo.2025.102275","url":null,"abstract":"<div><div><em>F</em>-Yang-Mills connections are critical points of <em>F</em>-Yang Mills functional on the space of connections of a principal fiber bundle, which are generalizations of Yang-Mills connections, <em>p</em>-Yang-Mills connections and exponential Yang-Mills connections and so on. Here, <em>F</em> is a strictly increasing <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-function. In this paper, we extend Simons theorem for the instability of Yang-Mills connections to <em>F</em>-Yang-Mills connections. We derive a sufficient condition that any non-flat, <em>F</em>-Yang-Mills connection over submanifolds in a Euclidean space is unstable. In the standard sphere case, this condition is expressed by an inequality involving its dimension and the degree of the differential of the function <em>F</em>. Our main results are proved by extending Kobayashi-Ohnita-Takeuchi's calculation to <em>F</em>-Yang-Mills connections.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102275"},"PeriodicalIF":0.7,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144867305","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
Manin triples on multiplicative Courant algebroids 乘法Courant代数上的Manin三元组
IF 0.7 4区 数学
Differential Geometry and its Applications Pub Date : 2025-08-01 DOI: 10.1016/j.difgeo.2025.102273
Ana Carolina Mançur
{"title":"Manin triples on multiplicative Courant algebroids","authors":"Ana Carolina Mançur","doi":"10.1016/j.difgeo.2025.102273","DOIUrl":"10.1016/j.difgeo.2025.102273","url":null,"abstract":"<div><div>We extend the characterization of Lie bialgebroids via Manin triples to the context of double structures over Lie groupoids. We consider Lie bialgebroid groupoids, given by LA-groupoids in duality, and establish their correspondence with multiplicative Manin triples, i.e., CA-groupoids equipped with a pair of complementary multiplicative Dirac structures. As an application, we give a new viewpoint to the co-quadratic Lie algebroids of Lang, Qiao, and Yin <span><span>[13]</span></span> and the Manin triple description of Lie bialgebroid crossed modules.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102273"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757592","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
Multisymplectic observable reduction using constraint triples 约束三元组的多辛可观察约简
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-07-16 DOI: 10.1016/j.difgeo.2025.102272
Antonio Michele Miti , Leonid Ryvkin
{"title":"Multisymplectic observable reduction using constraint triples","authors":"Antonio Michele Miti ,&nbsp;Leonid Ryvkin","doi":"10.1016/j.difgeo.2025.102272","DOIUrl":"10.1016/j.difgeo.2025.102272","url":null,"abstract":"<div><div>The purpose of this paper is to present a fully algebraic formalism for the construction and reduction of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebras of observables inspired by multisymplectic geometry, using Gerstenhaber algebras, BV-modules, and the constraint triple formalism. In the “geometric case”, we reconstruct and conceptually explain the recent results of <span><span>[7]</span></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102272"},"PeriodicalIF":0.6,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144634476","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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