On projectively flat Kropina metrics

Abstract

In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F={\alpha }^2/\beta$ with constant curvature $K$ and $\Vert \beta {\Vert }_{\alpha }=1$ is projectively flat if and only if $F$ is locally Minkowskian.

This paper has been withdrawn by the author due to a crucial improvement