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تسجيل مستخدم جديدEinstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds
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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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