In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.
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
Let （M, F） be a Finsler manifold, and let TMo be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of （TMo, G） and study ...Let （M, F） be a Finsler manifold, and let TMo be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of （TMo, G） and study their geometric properties. Next, we use this approach to obtain new characterizations of Finsler manifolds with positive constant flag curvature. We also investigate the relations between Levi-Civita connection, Cartan connection, Vaisman connection, vertical foliation, and Reinhart spaces.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities
文摘In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.
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.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11271304, 11671330, 11571288） and the Nanhu Scholars Program for Young Scholars of Xinyang Normal University.
文摘Let （M, F） be a Finsler manifold, and let TMo be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of （TMo, G） and study their geometric properties. Next, we use this approach to obtain new characterizations of Finsler manifolds with positive constant flag curvature. We also investigate the relations between Levi-Civita connection, Cartan connection, Vaisman connection, vertical foliation, and Reinhart spaces.
