Einstein Finsler metrics and killing vector fields on Riemannian manifolds |
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Authors: | XinYue Cheng ZhongMin Shen |
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Affiliation: | 1.School of Mathematics and Statistics,Chongqing University of Technology,Chongqing,China;2.Department of Mathematical Sciences,Indiana University-Purdue University,Indianapolis,USA |
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Abstract: | We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S 3 with Ric = 2F 2, Ric = 0 and Ric = -2F 2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not. |
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