In this paper,we consider the hypersurfaces of Randers space with constant flag curvature.(1)Let(M^n+1,F)be a Randers–Minkowski space.If(M^n,F)is a hypersurface of(M^n+1,F)with constant flag curvature K=1,then we can...In this paper,we consider the hypersurfaces of Randers space with constant flag curvature.(1)Let(M^n+1,F)be a Randers–Minkowski space.If(M^n,F)is a hypersurface of(M^n+1,F)with constant flag curvature K=1,then we can prove that M is Riemannian.(2)Let(M^n+1,F)be a Randers space with constant flag curvature.Assume(M,F)is a compact hypersurface of(M^n+1,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.展开更多
基金the National Natural Science Foundation of China(Grant No.11871405)。
文摘In this paper,we consider the hypersurfaces of Randers space with constant flag curvature.(1)Let(M^n+1,F)be a Randers–Minkowski space.If(M^n,F)is a hypersurface of(M^n+1,F)with constant flag curvature K=1,then we can prove that M is Riemannian.(2)Let(M^n+1,F)be a Randers space with constant flag curvature.Assume(M,F)is a compact hypersurface of(M^n+1,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.
