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.
Citation
Bin Shen. "Vanishing of Killing vector fields on compact Finsler manifolds." Kodai Math. J. 41 (1) 1 - 15, March 2018. https://doi.org/10.2996/kmj/1521424815