Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Vanishing of Killing vector fields on compact Finsler manifolds
Bin Shen
Author information
JOURNAL FREE ACCESS

2018 Volume 41 Issue 1 Pages 1-15

Details
Abstract

In this paper, we define a new Ricci curvature on Finsler manifold named the mean Ricci curvature, which is useful in the study of different symmetric fields on manifolds. By presenting a Bochner type formula of Killing vector fields on general Finsler manifolds, we prove the vanishing theorem of the Killing vector fields on any compact Finsler manifold with a negative mean Ricci curvature. This result involves the vanishing theorem of Killing vector fields in the Riemannian case.

Content from these authors

This article cannot obtain the latest cited-by information.

© 2018 Department of Mathematics, Tokyo Institute of Technology
Next article
feedback
Top