Abstract
With a volume form on a manifold, every spray can be deformed to a projective spray. The Riemann curvature of a projective spray is called the projective Riemmann curvature. In this paper, we introduce the notion of projectively R-flat sprays/Finsler metrics. As an application, we investigate and characterize projectively R-flat Randers metrics. Moreover, we obtained a rigidity theorem on a closed Finsler manifold.
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