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arXiv · 1207.1937

On Einstein Matsumoto metrics

Yi-Bing Shen·Xiaoling Zhang
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Abstract

In this paper, the necessary and sufficient conditions for Matsumoto metrics $F=\frac{α^2}{α-β}$ to be Einstein are given. It is shown that if the length of $β$ with respect to $α$ is constant, then the Matsumoto metric $F$ is an Einstein metric if and only if $α$ is Ricci-flat and $β$ is parallel with respect to $α$. A nontrivial example of Ricci flat Matsumoto metrics is given.

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Yi-Bing Shen, Xiaoling Zhang. 2012-07-09. On Einstein Matsumoto metrics. https://arxiv.org/abs/1207.1937

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