On Einstein Matsumoto metrics
Abstract
In this paper, the necessary and sufficient conditions for Matsumoto metrics F=α2α-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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