Some Theorems for Hypersurface of Randers Spaces

Abstract

In this paper, we consider the hypersurfaces of Randers space with constant flag curvature. (1) Let $({\overline M ^{n + 1}},\overline F )$ be a Randers-Minkowski space. If (Mⁿ, F)isa hypersurface of $({\overline M ^{n + 1}},\overline F )$ with constant flag curvature K = 1, then we can prove that M is Riemannian. (2) Let $({\overline M ^{n + 1}},\overline F )$ be a Randers space with constant flag curvature. Assume (M, F) is a compact hypersurface of $({\overline M ^{n + 1}},\overline F )$ with constant mean curvature ∣H∣. Then a pinching theorem is established, which generalizes the result of [Proc. Amer. Math. Soc., 120, 1223–1229 (1994)] from the Riemannian case to the Randers space.