Certain Conditions for a Finsler Manifold to Be Isometric with a Finsler Sphere

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2022-01-01 DOI:10.1515/agms-2022-0142

S. Yin, Huarong Wang

引用次数: 0

Abstract

Abstract We show that if there is a smooth function f on a Finsler n-space M satisfying Δ2f = −kfgΔf for a positive constant k, then M is diffeomorphic with the n-sphere 𝕊n, where g denotes the weighted Riemannian metric. Moreover, we further show that the manifold is isometric to a Finsler sphere if the Ricci curvature is bounded below by (n − [one.tf])k and the S-curvature vanishes.

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Finsler流形与Finsler球面等距的若干条件

摘要我们证明了如果在Finsler n空间M上存在一个光滑函数f，对于正常数k满足Δ2f =−kfgΔf，则M与n球𝕊n是微分同态的，其中g表示权黎曼度规。此外，我们进一步证明了如果里奇曲率以(n−[1 .tf])k为界且s曲率消失，流形与Finsler球是等距的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.