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 o...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.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11371386)the European Union’s Seventh Framework Programme (FP7/2007–2013) (Grant No. 317721)National Science Foundation of USA (Grant No. DMS-0810159)
文摘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.
