Randers Manifolds of Positive Constant Curvature

We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it. 1. Introduction. The geometry of Finsler manifolds of constant flag curvature is one of the fundamental subjects in Finsler geometry. Akbar-Zadeh [1] proved that, under some conditions on the growth of the Cartan tensor, a Finsler manifold of constant flag curvature K is locally Minkowskian if K = 0 and Riemannian if K = −1. So far, the case K > 0 is the least understood. Bryant [9] has constructed interesting Finsler metrics of positive constant flag curvature on the sphere S 2. Recently, Bao and Shen [5] constructed nonprojectively