A class of Finsler metrics with isotropic S-curvature
type: Item
instance of: scholarly article
title: A class of Finsler metrics with isotropic S-curvature
zbMATH Open document ID: 1165.53016
author: Zhongmin Shen
author: Xinyue Cheng
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: This paper studies the isotropic S-curvature of Finsler spaces with \((\alpha, \beta)\)-metric. A Randers space is a deformation of a Riemannian space \((M, \alpha)\) by a linear 1-form \(\beta\) such that \( F = \alpha + \beta\). The author studies the isotropic S-curvature of Randers type and obtains necessary and sufficient condition for isotropic S-curvature ( Theorem 1.1). This characterization is given by \((\alpha, \beta)\)-conditions only. Then the isotropic S-curvature of Finsler spaces with \((\alpha, \beta)\)-metric is investigated. The main novelty of the present paper is that it gives a characterization of isotropic S-curvature with \((\alpha, \beta)\)-metric ( Theorem 1.2). This characterization is given by \(\beta\)-conditions and \(\varphi(s)\)-conditions only. Also, the paper studies an ``almost isotropic S-curvature'' and ``constant S-curvature''.
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 5508743
reviewed by: Hideo Shimada
MaRDI profile type: Publication
full work available at URL: s11856-009-0013-1
OpenAlex ID: W2035021503
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DOI: 10.1007/S11856-009-0013-1
description: scientific article; zbMATH DE number 5508743