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arXiv · 1609.03055

Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds

Xinyue Cheng·Zhongmin Shen
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Abstract

In this paper, 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 ${\rm Ric} = 2 F^2$, ${\rm Ric}=0$ and ${\rm Ric}=- 2 F^2$, respectively. This family of metrics provide 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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Xinyue Cheng, Zhongmin Shen. 2016-09-10. Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds. https://doi.org/10.1007/s11425-016-0303-6

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