Differential Geometry and its Applications最新文献_第7页

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

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

引用次数: 0

The S-curvature of Finsler warped product metrics 芬斯勒扭曲积度量的 S曲率

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-26 DOI: 10.1016/j.difgeo.2023.102105

Mehran Gabrani , Bahman Rezaei , Esra Sengelen Sevim

引用次数: 0

Remarks on exact G2-structures on compact manifolds 关于紧凑流形上精确 G2 结构的评论

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-25 DOI: 10.1016/j.difgeo.2023.102101

Aaron Kennon

{"title":"Remarks on exact G2-structures on compact manifolds","authors":"Aaron Kennon","doi":"10.1016/j.difgeo.2023.102101","DOIUrl":"10.1016/j.difgeo.2023.102101","url":null,"abstract":"<div>An important open question related to the study of <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-holonomy manifolds concerns whether or not a compact seven-manifold can support an exact <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-structure. To provide insight into this question, we identify various relationships between the two-form underlying an exact <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-structure, the torsion of the <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-structure, and the curvatures of the associated metric. In addition to establishing identities valid for any hypothetical exact <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-structure, we also consider exact <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math>-structures subject to additional constraints, for instance proving incompatibility between the exact <math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and Extremally Ricci-Pinched conditions and establish new identities for soliton solutions of the Laplacian flow.</div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102101"},"PeriodicalIF":0.5,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585780","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

Prolongations, invariants, and fundamental identities of geometric structures 几何结构的延长线、不变式和基本同素异形体

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-16 DOI: 10.1016/j.difgeo.2023.102107

Jaehyun Hong , Tohru Morimoto

{"title":"Prolongations, invariants, and fundamental identities of geometric structures","authors":"Jaehyun Hong , Tohru Morimoto","doi":"10.1016/j.difgeo.2023.102107","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102107","url":null,"abstract":"<div>Working in the framework of nilpotent geometry, we give a unified scheme for the equivalence problem of geometric structures which extends and integrates the earlier works by Cartan, Singer-Sternberg, Tanaka, and Morimoto.By giving a new formulation of the higher order geometric structures and the universal frame bundles, we reconstruct the step prolongation of Singer-Sternberg and Tanaka. We then investigate the structure function γ of the complete step prolongation of a proper geometric structure by expanding it into components <math><mi>γ</mi><mo>=</mo><mi>κ</mi><mo>+</mo><mi>τ</mi><mo>+</mo><mi>σ</mi></math> and establish the fundamental identities for κ, τ, σ. This then enables us to study the equivalence problem of geometric structures in full generality and to extend applications largely to the geometric structures which have not necessarily Cartan connections.Among all we give an algorithm to construct a complete system of invariants for any higher order proper geometric structure of constant symbol by making use of generalized Spencer cohomology group associated to the symbol of the geometric structure. We then discuss thoroughly the equivalence problem for geometric structure in both cases of infinite and finite type.We also give a characterization of the Cartan connections by means of the structure function τ and make clear where the Cartan connections are placed in the perspective of the step prolongations.</div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"92 ","pages":"Article 102107"},"PeriodicalIF":0.5,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139480185","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

Traveling along horizontal broken geodesics of a homogeneous Finsler submersion 沿均质芬斯勒淹没的水平断裂大地线行进

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-15 DOI: 10.1016/j.difgeo.2023.102106

Marcos M. Alexandrino, Fernando M. Escobosa, Marcelo K. Inagaki

{"title":"Traveling along horizontal broken geodesics of a homogeneous Finsler submersion","authors":"Marcos M. Alexandrino, Fernando M. Escobosa, Marcelo K. Inagaki","doi":"10.1016/j.difgeo.2023.102106","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102106","url":null,"abstract":"<div>In this paper, we discuss how to travel along horizontal broken geodesics of a homogeneous Finsler submersion, i.e., we study, what in Riemannian geometry was called by Wilking, the dual leaves. More precisely, we investigate the attainable sets <math><msub><mrow><mi>A</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>C</mi><mo>)</mo></math> of the set of analytic vector fields <math><mi>C</mi></math> determined by the family of horizontal unit geodesic vector fields <math><mi>C</mi></math> to the fibers <math><mi>F</mi><mo>=</mo><mo>{</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mi>c</mi><mo>)</mo><mo>}</mo></math> of a homogeneous analytic Finsler submersion <math><mi>ρ</mi><mo>:</mo><mi>M</mi><mo>→</mo><mi>B</mi></math>. Since reverse of geodesics don't need to be geodesics in Finsler geometry, one can have examples on non compact Finsler manifolds M where the attainable sets (the dual leaves) are no longer orbits or even submanifolds. Nevertheless we prove that, when M is compact and the orbits of <math><mi>C</mi></math> are embedded, then the attainable sets coincide with the orbits. Furthermore, if the flag curvature is positive then M coincides with the attainable set of each point. In other words, fixed two points of M, one can travel from one point to the other along horizontal broken geodesics.In addition, we show that each orbit <math><mi>O</mi><mo>(</mo><mi>q</mi><mo>)</mo></math> of <math><mi>C</mi></math> associated to a singular Finsler foliation coincides with M, when the flag curvature is positive, i.e., we prove Wilking's result in Finsler context. In particular we review Wilking's transversal Jacobi fields in Finsler case.</div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102106"},"PeriodicalIF":0.5,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139467784","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 normal line congruence and minimal ruled Lagrangian submanifolds in CPn CPn 中的法线全等和最小规则拉格朗日子平面

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-09 DOI: 10.1016/j.difgeo.2023.102099

Jong Taek Cho , Makoto Kimura

引用次数: 0

Antipodal sets of pseudo-Riemannian symmetric R-spaces 伪黎曼对称 R 空间的对偶集

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-08 DOI: 10.1016/j.difgeo.2023.102104

Kyoji Sugimoto

引用次数: 0

On the prescribed fractional Q-curvatures problem on Sn under pinching conditions 关于捏合条件下 Sn 上的规定分数 Q 曲线问题

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-03 DOI: 10.1016/j.difgeo.2023.102103

Zhongwei Tang , Ning Zhou

引用次数: 0

When are shrinking gradient Ricci soliton compact 什么时候收缩梯度利玛窦孤子是紧凑的？

IF 0.5 4区数学

Differential Geometry and its Applications Pub Date : 2024-01-02 DOI: 10.1016/j.difgeo.2023.102102

Yuanyuan Qu, Guoqiang Wu

引用次数: 0