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Differential Geometry and its Applications最新文献

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A note on the shifted Courant-Nijenhuis torsion 关于移位库朗-尼延胡斯扭转的说明
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-03-18 DOI: 10.1016/j.difgeo.2024.102120
Marco Aldi , Sergio Da Silva , Daniele Grandini
{"title":"A note on the shifted Courant-Nijenhuis torsion","authors":"Marco Aldi ,&nbsp;Sergio Da Silva ,&nbsp;Daniele Grandini","doi":"10.1016/j.difgeo.2024.102120","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102120","url":null,"abstract":"<div><p>We characterize the vanishing of the shifted Courant-Nijenhuis torsion as the strongest tensorial integrability condition that can be imposed on a skew-symmetric endomorphism of the generalized tangent bundle.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102120"},"PeriodicalIF":0.5,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140160508","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 statistical submersions from 3-Sasakian statistical manifolds 论来自 3-Sasakian 统计流形的统计潜流
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-03-18 DOI: 10.1016/j.difgeo.2024.102124
Mohammad Bagher Kazemi Balgeshir, Shiva Salahvarzi
{"title":"On statistical submersions from 3-Sasakian statistical manifolds","authors":"Mohammad Bagher Kazemi Balgeshir,&nbsp;Shiva Salahvarzi","doi":"10.1016/j.difgeo.2024.102124","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102124","url":null,"abstract":"<div><p>In this paper, we define and characterize 3-Sasakian statistical manifolds and then investigate statistical submersions from 3-Sasakian statistical manifolds. We prove that invariant statistical submersions from 3-Sasakian statistical manifolds with vertical structure vector fields have 3-Sasakian statistical totally geodesic fibers. Moreover, the base space admits a quaternionic Kähler statistical structure. We construct non-trivial examples to illustrate some results of the paper.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102124"},"PeriodicalIF":0.5,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140160507","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 new perspective on border completion in visual cortex as bicycle rear wheel geodesics paths via sub Riemannian Hamiltonian formalism 通过子黎曼哈密顿形式主义，以自行车后轮大地路径为视皮层边界完成的新视角
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-03-15 DOI: 10.1016/j.difgeo.2024.102125
R. Fioresi , A. Marraffa , J. Petkovic
{"title":"A new perspective on border completion in visual cortex as bicycle rear wheel geodesics paths via sub Riemannian Hamiltonian formalism","authors":"R. Fioresi ,&nbsp;A. Marraffa ,&nbsp;J. Petkovic","doi":"10.1016/j.difgeo.2024.102125","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102125","url":null,"abstract":"<div><p>We present a review of known models and a new simple mathematical modelling for border completion in the visual cortex V1 highlighting the striking analogies with bicycle rear wheel motions in the plane.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102125"},"PeriodicalIF":0.5,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140134564","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
Gromoll–Meyer's actions and the geometry of (exotic) spacetimes 格罗莫尔-迈耶行动与（奇异）时空几何
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-03-13 DOI: 10.1016/j.difgeo.2024.102121
Leonardo F. Cavenaghi, Lino Grama
{"title":"Gromoll–Meyer's actions and the geometry of (exotic) spacetimes","authors":"Leonardo F. Cavenaghi,&nbsp;Lino Grama","doi":"10.1016/j.difgeo.2024.102121","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102121","url":null,"abstract":"<div><p>Since the advent of new pairwise non-diffeomorphic structures on smooth manifolds, it has been questioned whether two topologically identical manifolds could admit different geometries. Not surprisingly, physicists have wondered whether a different smooth structure assumption to some classical known model could produce different physical meanings. Motivated by the works <span>[27]</span>, <span>[2]</span>, <span>[3]</span>, <span>[18]</span>, in this paper, we inaugurate a very computational manner to produce physical models on classical and exotic spheres that can be built equivariantly, such as the classical Gromoll–Meyer exotic spheres. As first applications, we produce Lorentzian metrics on homeomorphic but not diffeomorphic manifolds that enjoy the same physical properties, such as geodesic completeness, positive Ricci curvature, and compatible time orientation. These constructions can be pulled back to higher models, such as exotic ten spheres bounding spin manifolds, to be approached in forthcoming papers.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102121"},"PeriodicalIF":0.5,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140123176","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
Structures of sympathetic Lie conformal superalgebras 交感列共形上代数的结构
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-03-12 DOI: 10.1016/j.difgeo.2024.102122
Meher Abdaoui
{"title":"Structures of sympathetic Lie conformal superalgebras","authors":"Meher Abdaoui","doi":"10.1016/j.difgeo.2024.102122","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102122","url":null,"abstract":"<div><p>In this paper, we'll introduce the concept of sympathetic Lie conformal superalgebras and show that some classical properties of Lie conformal superalgebras are still valid for sympathetic Lie conformal superalgebras. We prove that the unique decomposition of each sympathetic Lie conformal superalgebra into a direct sum of indecomposable sympathetic ideals. We also show the existence of a greatest sympathetic ideal and a sympathetic decomposition in every perfect Lie conformal superalgebra. In the end, we also study the ideal <span><math><mi>I</mi></math></span> of a Lie conformal superalgebra <span><math><mi>R</mi></math></span> such that <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> is a sympathetic Lie conformal superalgebra.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"94 ","pages":"Article 102122"},"PeriodicalIF":0.5,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140104001","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
Convergence rate of the weighted Yamabe flow 加权山边流的收敛率
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-02-28 DOI: 10.1016/j.difgeo.2024.102119
Pak Tung Ho , Jinwoo Shin , Zetian Yan
{"title":"Convergence rate of the weighted Yamabe flow","authors":"Pak Tung Ho ,&nbsp;Jinwoo Shin ,&nbsp;Zetian Yan","doi":"10.1016/j.difgeo.2024.102119","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102119","url":null,"abstract":"<div><p>The weighted Yamabe flow is the geometric flow introduced to study the weighted Yamabe problem on smooth metric measure spaces. Carlotto, Chodosh and Rubinstein have studied the convergence rate of the Yamabe flow. Inspired by their result, we study in this paper the convergence rate of the weighted Yamabe flow.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102119"},"PeriodicalIF":0.5,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139993169","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 weakly stretch Kropina metrics 关于弱伸展的克罗皮纳度量
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-02-21 DOI: 10.1016/j.difgeo.2024.102118
A. Tayebi, F. Barati
{"title":"On weakly stretch Kropina metrics","authors":"A. Tayebi,&nbsp;F. Barati","doi":"10.1016/j.difgeo.2024.102118","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102118","url":null,"abstract":"<div><p>In this paper, we study weakly stretch Kropina metrics and prove a rigidity theorem. We show that the associated one-form of a weakly stretch Kropina metric is conformally Killing with respect to the associated Riemannian metric. We find that any weakly stretch Kropina metric has vanishing S-curvature. Then, we prove that every weakly stretch Kropina metric is a Berwald metric. It turns out that every R-quadratic Kropina metric is a Berwald metric. Finally, we show that every positively complete C-reducible metric is R-quadratic if and only if it is Berwaldian.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102118"},"PeriodicalIF":0.5,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139914480","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
Landsberg Finsler warped product metrics with zero flag curvature 具有零旗曲率的兰茨贝格-芬斯勒翘曲积度量
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-02-21 DOI: 10.1016/j.difgeo.2023.102082
Daxiao Zheng
{"title":"Landsberg Finsler warped product metrics with zero flag curvature","authors":"Daxiao Zheng","doi":"10.1016/j.difgeo.2023.102082","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102082","url":null,"abstract":"<div><p>In this paper, we study Finsler warped product metrics. We obtain the differential equations that characterize Landsberg Finsler warped product metrics. By solving these equations, we obtain the expression of these metrics. Furthermore, we construct a class of almost regular Finsler warped product metrics <em>F</em> with the following properties: (1) <em>F</em> is a Landsberg metric; (2) <em>F</em> is not a Berwald metric; (3) <em>F</em> has zero flag curvature (or Ricci curvature).</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102082"},"PeriodicalIF":0.5,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139936016","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 category of Z−graded manifolds: What happens if you do not stay positive Z级流形的范畴：不保持正向会发生什么
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-02-01 DOI: 10.1016/j.difgeo.2024.102109
Alexei Kotov , Vladimir Salnikov
{"title":"The category of Z−graded manifolds: What happens if you do not stay positive","authors":"Alexei Kotov ,&nbsp;Vladimir Salnikov","doi":"10.1016/j.difgeo.2024.102109","DOIUrl":"10.1016/j.difgeo.2024.102109","url":null,"abstract":"<div><p>In this paper we discuss the categorical properties of <span><math><mi>Z</mi></math></span>-graded manifolds. We start by describing the local model paying special attention to the differences in comparison to the <span><math><mi>N</mi></math></span>-graded case. In particular we explain the origin of formality for the functional space and spell-out the structure of the power series. Then we make this construction intrinsic using a new type of filtrations. This sums up to proper definitions of objects and morphisms in the category. We also formulate the analog of the Borel's lemma for the functional spaces on <span><math><mi>Z</mi></math></span>-graded manifolds and the analogue of Batchelor's theorem for the global structure of them.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102109"},"PeriodicalIF":0.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0926224524000020/pdfft?md5=a5f043ddb99e39117ce84444d49aff31&pid=1-s2.0-S0926224524000020-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139667841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On homogeneous closed gradient Laplacian solitons 关于同质封闭梯度拉普拉卡孤子
IF 0.5 4区 数学
Differential Geometry and its Applications Pub Date : 2024-01-31 DOI: 10.1016/j.difgeo.2024.102108
Nicholas Ng
{"title":"On homogeneous closed gradient Laplacian solitons","authors":"Nicholas Ng","doi":"10.1016/j.difgeo.2024.102108","DOIUrl":"https://doi.org/10.1016/j.difgeo.2024.102108","url":null,"abstract":"<div><p>We prove a structure theorem for homogeneous closed gradient Laplacian solitons and use it to show some examples of closed Laplacian solitons cannot be made gradient. More specifically, we show that the Laplacian solitons on nilpotent Lie groups found by Nicolini are not gradient up to homothetic <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structures except for <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>7</mn></mrow></msup></math></span>, where the potential function must be of a certain form. We also show that one of the closed <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structures constructed by Fernández-Fino-Manero cannot be a gradient soliton. We then examine the structure of almost abelian solvmanifolds admitting closed non-torsion-free gradient Laplacian solitons.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102108"},"PeriodicalIF":0.5,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139653196","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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