On Obata theorem in Randers spaces

The classical Obata theorem in Riemannian space is generalized to the Randers spaces. It is proved that, if the generalized Obata equation on a closed Douglas Randers spaces admits a nontrivial solution, then M is weakly isometric to the Euclidean sphere (S-n (1), h), where, h denotes the standard Riemannian metric of S-n (1). In particular, F is locally projectively flat with positive flag curvature. (C) 2016 Elsevier B.V. All rights reserved.