A Kähler structure on Finsler spaces with nonzero constant flag curvature

Abstract

In this paper, we obtain a Kähler structure on the tangent bundle of a Finsler manifold of positive constant flag curvature. We show that there does not exist any Finsler metric such that this structure became locally symmetric or Einstein manifold. Similar results are obtained on a tube around zero section in the tangent bundle in the case of a Finsler manifold of negative constant flag curvature.