Compact surfaces of constant Gaussian curvature in Randers manifolds

Abstract

The flag curvature of a Finsler surface is called the Gaussian curvature in Finsler geometry. In this paper, we characterize the surfaces of constant Gaussian curvature (CGC) in the Randers 3-manifold. Then we give a classification of the orientable closed CGC surfaces in two Randers space forms, which are the non-Euclidean Minkowski–Randers 3-space ( K = 0 ) and the Bao–Shen sphere ( K = 1 ).