具有零旗曲率的兰茨贝格-芬斯勒翘曲积度量

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-02-21 DOI:10.1016/j.difgeo.2023.102082

Daxiao Zheng

{"title":"具有零旗曲率的兰茨贝格-芬斯勒翘曲积度量","authors":"Daxiao Zheng","doi":"10.1016/j.difgeo.2023.102082","DOIUrl":null,"url":null,"abstract":"<div>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 F with the following properties: (1) F is a Landsberg metric; (2) F is not a Berwald metric; (3) F has zero flag curvature (or Ricci curvature).</div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"93 ","pages":"Article 102082"},"PeriodicalIF":0.6000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Landsberg Finsler warped product metrics with zero flag curvature\",\"authors\":\"Daxiao Zheng\",\"doi\":\"10.1016/j.difgeo.2023.102082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>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 F with the following properties: (1) F is a Landsberg metric; (2) F is not a Berwald metric; (3) F has zero flag curvature (or Ricci curvature).</div>\",\"PeriodicalId\":51010,\"journal\":{\"name\":\"Differential Geometry and its Applications\",\"volume\":\"93 \",\"pages\":\"Article 102082\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Geometry and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224523001080\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001080","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究 Finsler 翘积度量。我们得到了表征兰茨贝格-芬斯勒翘曲积度量的微分方程。通过求解这些方程，我们得到了这些度量的表达式。此外，我们还构建了一类几乎正则的 Finsler 翘积度量 F，它们具有以下性质：（1）F 是一个 Landsberg 度量；（2）F 不是一个 Berwald 度量；（3）F 的旗曲率（或里奇曲率）为零。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Landsberg Finsler warped product metrics with zero flag curvature

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 F with the following properties: (1) F is a Landsberg metric; (2) F is not a Berwald metric; (3) F has zero flag curvature (or Ricci curvature).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.