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Differential Geometry and its Applications最新文献

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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
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
{"title":"The S-curvature of Finsler warped product metrics","authors":"Mehran Gabrani ,&nbsp;Bahman Rezaei ,&nbsp;Esra Sengelen Sevim","doi":"10.1016/j.difgeo.2023.102105","DOIUrl":"10.1016/j.difgeo.2023.102105","url":null,"abstract":"<div><p>The class of warped product metrics can often be interpreted as key space models for general theory of relativity and in the theory of space-time structure. In this paper, we study one of the most important non-Riemannian quantities in Finsler geometry which is called the S-curvature. We examined the behavior of the S-curvature in the Finsler warped product metrics. We are going to prove that every Finsler warped product metric <span><math><mi>R</mi><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> has almost isotropic <em>S</em>-curvature if and only if it is a weakly Berwald metric. Moreover, we show that every Finsler warped product metric has isotropic <em>S</em>-curvature if and only if <em>S</em>-curvature vanishes.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102105"},"PeriodicalIF":0.5,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585862","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
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><p>An important open question related to the study of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-holonomy manifolds concerns whether or not a compact seven-manifold can support an exact <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structure. To provide insight into this question, we identify various relationships between the two-form underlying an exact <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structure, the torsion of the <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structure, and the curvatures of the associated metric. In addition to establishing identities valid for any hypothetical exact <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structure, we also consider exact <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-structures subject to additional constraints, for instance proving incompatibility between the exact <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span><span> and Extremally Ricci-Pinched conditions and establish new identities for soliton solutions of the Laplacian flow.</span></p></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 ,&nbsp;Tohru Morimoto","doi":"10.1016/j.difgeo.2023.102107","DOIUrl":"https://doi.org/10.1016/j.difgeo.2023.102107","url":null,"abstract":"<div><p>Working in the framework of nilpotent<span> 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.</span></p><p>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 <em>γ</em> of the complete step prolongation of a proper geometric structure by expanding it into components <span><math><mi>γ</mi><mo>=</mo><mi>κ</mi><mo>+</mo><mi>τ</mi><mo>+</mo><mi>σ</mi></math></span> and establish the fundamental identities for <em>κ</em>, <em>τ</em>, <em>σ</em>. 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.</p><p>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.</p><p>We also give a characterization of the Cartan connections by means of the structure function <em>τ</em> and make clear where the Cartan connections are placed in the perspective of the step prolongations.</p></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
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