Certain conditions for a Finsler manifold to be isometric with a Finsler sphere
type: Item
instance of: scholarly article
title: Certain conditions for a Finsler manifold to be isometric with a Finsler sphere
zbMATH Open document ID: 1505.53084
author: Huarong Wang
author: Songting Yin
published in: Analysis and Geometry in Metric Spaces
publication date: 2022-10-21T00:00:00Z
review text: The authors state that a Finsler manifold \((M,F)\) is diffeomorphic to the \(n\)-dimensional sphere whenever there exists a smooth function on \(M\) satisfying \(\nabla^2f=-kfg_{\nabla_f}\) for a positive constant \(k\). Here \(g_{\nabla_f}=g_{ij}(x,\nabla f)dx^i\otimes dx^j\), where\(g_{ij}=\frac{1}{2}[F^2]_{y^iy^j}\) and \((x^i,y^i)\) are the local coordinates on the tangent bundle of \(M\).
reviewed by: Mohammed El Aïdi
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 7604613
zbMATH Keywords: Finsler sphere
zbMATH Keywords: weighted Ricci curvature
MaRDI profile type: Publication
full work available at URL: agms-2022-0142
OpenAlex ID: W4312816537
Wikidata QID: Q125567271
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DOI: 10.1515/AGMS-2022-0142
description: scientific article; zbMATH DE number 7604613