On Conformal Vector Fields of a Class of Finsler Spaces I

Guojun Yang

Published 2014-04-13, updated 2016-08-27Version 2

An $(\alpha,\beta)$-metric is defined by a Riemannian metric $\alpha$ and $1$-form $\beta$. In this paper, we characterize conformal vector fields of $(\alpha,\beta)$-spaces by some PDEs. Further, we determine the local solutions of conformal vector fields of $(\alpha,\beta)$-spaces in dimension $n\ge 3$ under certain curvature conditions. In addition, we use certain conformal vector field to give a new proof to a known result on the local and global classifications for Randers metrics which are locally projectively flat and of isotropic S-curvature.