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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 : 2025-09-01 Epub 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":"2025-09-01","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
A remark on deformation of Gromov non-squeezing 关于Gromov非挤压变形的评述
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-06-02 DOI: 10.1016/j.difgeo.2025.102262
Yasha Savelyev
{"title":"A remark on deformation of Gromov non-squeezing","authors":"Yasha Savelyev","doi":"10.1016/j.difgeo.2025.102262","DOIUrl":"10.1016/j.difgeo.2025.102262","url":null,"abstract":"<div><div>Let <span><math><mi>R</mi><mo>,</mo><mi>r</mi></math></span> be as in the classical Gromov non-squeezing theorem, and let <span><math><mi>ϵ</mi><mo>=</mo><mo>(</mo><mi>π</mi><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>π</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>/</mo><mi>π</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We first conjecture that the Gromov non-squeezing phenomenon persists for deformations of the symplectic form on the range <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> (w.r.t. the standard metric) <em>ϵ</em>-nearby to the standard symplectic form. We prove this in some special cases, in particular when the dimension is four and when <span><math><mi>R</mi><mo>&lt;</mo><msqrt><mrow><mn>2</mn></mrow></msqrt><mi>r</mi></math></span>. Given such a perturbation, we can no longer compactify the range and hence the classical Gromov argument breaks down. Our main method consists of a certain trap idea for holomorphic curves, analogous to traps in dynamical systems.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102262"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144190117","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
Principal bundles in the category of Z2n-manifolds z2n -流形范畴中的主束
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-07-09 DOI: 10.1016/j.difgeo.2025.102269
Andrew James Bruce , Janusz Grabowski
{"title":"Principal bundles in the category of Z2n-manifolds","authors":"Andrew James Bruce ,&nbsp;Janusz Grabowski","doi":"10.1016/j.difgeo.2025.102269","DOIUrl":"10.1016/j.difgeo.2025.102269","url":null,"abstract":"<div><div>We introduce and examine the notion of principal <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-bundles, i.e., principal bundles in the category of <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-manifolds. The latter are higher graded extensions of supermanifolds in which a <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-grading replaces <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-grading. These extensions have opened up new areas of research of great interest in both physics and mathematics. In principle, the geometry of <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-manifolds is essentially different than that of supermanifolds, as for n &gt; 1 we have formal variables of even parity, so local smooth functions are power series in formal variables. On the other hand, a full version of differential calculus is still valid. We show in this paper that the fundamental properties of classical principal bundles can be generalised to the setting of this ‘higher graded’ geometry, with properly defined frame bundles of <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-vector bundles as canonical examples. Additionally, we propose a new approach to the concept of a vector bundle in this setting. However, formulating these ideas and proving these results relies on many technical upshots established in earlier papers. A comprehensive introduction to <span><math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>-manifolds is therefore included together with basic examples.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102269"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579541","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 : 2025-09-01 Epub 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":"2025-09-01","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
Some vanishing theorems for p-harmonic l-forms on complete Riemannian manifolds 完备黎曼流形上p调和l型的消失定理
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-06-25 DOI: 10.1016/j.difgeo.2025.102267
Nan Li, Zhenghan Shen
{"title":"Some vanishing theorems for p-harmonic l-forms on complete Riemannian manifolds","authors":"Nan Li,&nbsp;Zhenghan Shen","doi":"10.1016/j.difgeo.2025.102267","DOIUrl":"10.1016/j.difgeo.2025.102267","url":null,"abstract":"<div><div>In this paper, we give some vanishing theorems for <em>p</em>-harmonic <em>l</em>-forms on complete non-compact Riemannian manifolds. Firstly, we prove a vanishing theorem on Riemannian manifolds with nonnegative scalar curvature and a more general upper bound of pointwise curvature condition. Secondly, by using the similar trick, we obtain some vanishing theorems on complete immersed submanifold of Euclidean space.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102267"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471724","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 : 2025-09-01 Epub 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":"2025-09-01","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
C1-isometric embeddings of Riemannian spaces in Lorentzian spaces 洛伦兹空间中黎曼空间的c1等距嵌入
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-06-25 DOI: 10.1016/j.difgeo.2025.102266
Alaa Boukholkhal
{"title":"C1-isometric embeddings of Riemannian spaces in Lorentzian spaces","authors":"Alaa Boukholkhal","doi":"10.1016/j.difgeo.2025.102266","DOIUrl":"10.1016/j.difgeo.2025.102266","url":null,"abstract":"<div><div>For any compact Riemannian manifold <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mi>g</mi><mo>)</mo></math></span> and any Lorentzian manifold <span><math><mo>(</mo><mi>W</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>, we prove that any spacelike embedding <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>→</mo><mi>W</mi></math></span> that is long (<span><math><mi>g</mi><mo>≤</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>h</mi></math></span>) can be <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-approximated by a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> isometric embedding <span><math><mi>F</mi><mo>:</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>g</mi><mo>)</mo><mo>→</mo><mo>(</mo><mi>W</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102266"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471655","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 cohomogeneity one hyperpolar actions related to G2 关于同质性的一个与G2有关的超极性作用
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-07-15 DOI: 10.1016/j.difgeo.2025.102271
Shinji Ohno , Yuuki Sasaki
{"title":"On cohomogeneity one hyperpolar actions related to G2","authors":"Shinji Ohno ,&nbsp;Yuuki Sasaki","doi":"10.1016/j.difgeo.2025.102271","DOIUrl":"10.1016/j.difgeo.2025.102271","url":null,"abstract":"<div><div>Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and exceptional actions. In this paper, we consider exceptional actions related to the exceptional compact Lie group <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and investigate some properties of their orbits as Riemannian submanifolds. In particular, we examine the principal curvatures of principal orbits and classify principal orbits that are minimal, austere, weakly reflective, and proper biharmonic.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102271"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631296","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 Alexandrov theorems in spacetimes with integral conditions 具有积分条件的时空中的广义Alexandrov定理
IF 0.6 4区 数学
Differential Geometry and its Applications Pub Date : 2025-09-01 Epub Date: 2025-05-14 DOI: 10.1016/j.difgeo.2025.102254
Kwok-Kun Kwong , Xianfeng Wang
{"title":"Generalized Alexandrov theorems in spacetimes with integral conditions","authors":"Kwok-Kun Kwong ,&nbsp;Xianfeng Wang","doi":"10.1016/j.difgeo.2025.102254","DOIUrl":"10.1016/j.difgeo.2025.102254","url":null,"abstract":"<div><div>We investigate integral conditions involving the mean curvature vector <span><math><mover><mrow><mi>H</mi></mrow><mrow><mo>→</mo></mrow></mover></math></span> or mixed higher-order mean curvatures, to determine when a codimension-two submanifold Σ lies on a shear-free (umbilical) null hypersurface in a spacetime. We generalize the Alexandrov-type theorems in spacetime introduced in <span><span>[18]</span></span> by relaxing the curvature conditions on Σ in several aspects. Specifically, we provide a necessary and sufficient condition, in terms of a mean curvature integral inequality, for Σ to lie in a shear-free null hypersurface. A key component of our approach is the use of Minkowski formulas with arbitrary weight, which enables us to derive rigidity results for submanifolds with significantly weaker integral curvature conditions.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"100 ","pages":"Article 102254"},"PeriodicalIF":0.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941901","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 : 2025-09-01 Epub 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":"2025-09-01","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
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