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Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds
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
with , and ,
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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