A class of Finsler metrics with isotropic S-curvature
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''.
scientific article; zbMATH DE number 5508743
scientific article