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SOME RESULTS ON THE NON-RIEMANNIAN QUANTITY H OF A FINSLER METRIC

QIAOLING XIA

Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang Province, P. R. China

https://doi.org/10.1142/S0129167X11007082Cited by:10 (Source: Crossref)

Abstract

In this paper, we study the non-Riemannian quantity H in Finsler geometry. We obtain some rigidity theorems of a compact Finsler manifold under some conditions related to H. We also prove that the S-curvature for a Randers metric is almost isotropic if and only if H almost vanishes. In particular, S-curvature is isotropic if and only if H = 0.

Keywords:

AMSC: 58B20, 53C60

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