English

On Einstein Matsumoto metrics

Differential Geometry 2012-07-10 v1

Abstract

In this paper, the necessary and sufficient conditions for Matsumoto metrics F=α2αβF=\frac{\alpha^2}{\alpha-\beta} to be Einstein are given. It is shown that if the length of β\beta with respect to α\alpha is constant, then the Matsumoto metric FF is an Einstein metric if and only if α\alpha is Ricci-flat and β\beta is parallel with respect to α\alpha. 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}
}
R2 v1 2026-06-21T21:32:32.138Z