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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1016/0029-5493(89)90192-1

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1869-1862

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On Einstein Matsumoto metrics

Authors: XiaoLing Zhang QiaoLing Xia
Publish Date: 2014/02/26
Volume: 57, Issue: 7, Pages: 1517-1524
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Abstract

We study a special class of Finsler metrics namely Matsumoto metrics F = tfracalpha 2 alpha beta where α is a Riemannian metric and β is a 1form on a manifold M We prove that F is a weak Einstein metric if and only if α is Ricci flat and β is a parallel 1form with respect to α In this case F is Ricci flat and Berwaldian As an application we determine the local structure and prove the 3dimensional rigidity theorem for a weak Einstein Matsumoto metric

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