Finsler流形与Finsler球面等距的若干条件

Pub Date : 2022-01-01 DOI:10.1515/agms-2022-0142

S. Yin, Huarong Wang

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引用次数: 0

摘要

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。

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

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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