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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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11371386), the European Union’s Seventh Framework Programme (FP7/2007–2013) (Grant No. 317721) and National Science Foundation of USA (Grant No. DMS-0810159).
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Cheng, X., Shen, Z. Einstein Finsler metrics and killing vector fields on Riemannian manifolds. Sci. China Math. 60, 83–98 (2017). https://doi.org/10.1007/s11425-016-0303-6
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DOI: https://doi.org/10.1007/s11425-016-0303-6