On Einstein Matsumoto metrics
Differential Geometry
2012-07-10 v1
Abstract
In this paper, the necessary and sufficient conditions for Matsumoto metrics to be Einstein are given. It is shown that if the length of with respect to is constant, then the Matsumoto metric is an Einstein metric if and only if is Ricci-flat and is parallel with respect to . A nontrivial example of Ricci flat Matsumoto metrics is given.
Cite
@article{arxiv.1207.1937,
title = {On Einstein Matsumoto metrics},
author = {Yi-Bing Shen and Xiaoling Zhang},
journal= {arXiv preprint arXiv:1207.1937},
year = {2012}
}