Compact surfaces of constant Gaussian curvature in Randers manifolds

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=0K=0) and the Bao–Shen sphere (K=1K=1).