On a class of weakly Einstein Finsler metrics |
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Authors: | Zhongmin Shen Guojun Yang |
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Institution: | 1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis (IUPUI), 402 N. Blackford Street, Indianapolis, IN, 46202-3216, USA 2. Department of Mathematics, Sichuan University, Chengdu, 610064, P. R. China
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Abstract: | In this paper we study a special class of Finsler metrics—m-Kropina metrics which are defined by a Riemannian metric and a 1-form. We prove that a weakly Einstein m-Kropina metric must be Einsteinian. Further, we characterize Einstein m-Kropina metrics in very simple conditions under a suitable deformation, and obtain the local structures of m-Kropina metrics which are of constant flag curvature and locally projectively flat with constant flag curvature respectively. |
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