Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds
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2017-01
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English
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Springer
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 S3 with Ric = 2F2, Ric = 0 and Ric = -2F2, 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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Cheng, X., & Shen, Z. (2017). Einstein Finsler metrics and killing vector fields on Riemannian manifolds. Science China Mathematics, 60(1), 83-98. doi:10.1007/s11425-016-0303-6
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Science China Mathematics
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ArXiv
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Author's manuscript