Let(M, F) be an n-dimensional Randers space with scalar flag curvature. In this paper, we will introduce the definition of a weak Einstein manifold. We can prove that if(M, F) is a weak Einstein manifold, then the fla...Let(M, F) be an n-dimensional Randers space with scalar flag curvature. In this paper, we will introduce the definition of a weak Einstein manifold. We can prove that if(M, F) is a weak Einstein manifold, then the flag curvature is constant.展开更多
The contribution of this paper is second-fold.The first one is to derive the HTminimal hypersurfaces of rotation in special Randers spaces,which are non-Minkowski but have vanishing flag curvatures.The second one is t...The contribution of this paper is second-fold.The first one is to derive the HTminimal hypersurfaces of rotation in special Randers spaces,which are non-Minkowski but have vanishing flag curvatures.The second one is to characterize the anisotropic minimal rotational hypersurfaces in Funk spaces.展开更多
Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is ...Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.展开更多
In this paper,we study conformal vector fields on a Randers manifold with certain curvature properties.In particular,we completely determine conformal vector fields on a Randers manifold of weakly isotropic flag curva...In this paper,we study conformal vector fields on a Randers manifold with certain curvature properties.In particular,we completely determine conformal vector fields on a Randers manifold of weakly isotropic flag curvature.展开更多
In this paper, we study a class of Finsler metrics defined by a vector field on a Riemannian space form. We give an explicit formula for those with isotropic S-curvature. This class contains all Randers metrics of con...In this paper, we study a class of Finsler metrics defined by a vector field on a Riemannian space form. We give an explicit formula for those with isotropic S-curvature. This class contains all Randers metrics of constant flag curvature.展开更多
基金supported by NSFC(No.11471246)Natural Science Foundation of Anhui Province(No.1608085MA03)Natural Science Foundation of Higher Education in Anhui Province(No.KJ2014A257)
基金supported by the National Natural Science Foundation of China (11871405)。
文摘Let(M, F) be an n-dimensional Randers space with scalar flag curvature. In this paper, we will introduce the definition of a weak Einstein manifold. We can prove that if(M, F) is a weak Einstein manifold, then the flag curvature is constant.
文摘The contribution of this paper is second-fold.The first one is to derive the HTminimal hypersurfaces of rotation in special Randers spaces,which are non-Minkowski but have vanishing flag curvatures.The second one is to characterize the anisotropic minimal rotational hypersurfaces in Funk spaces.
文摘Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized (α, β) - metric ( μ1, μ2 and μ3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized (α, β) -metric F has some curvature property.
基金supported by National Science Foundation of USA (Grant No. DMS-0810159)National Natural Science Foundation of China (Grant No. 11171297)Natural Science Foundationof Zhejiang Province (Grant No. Y6110027)
文摘In this paper,we study conformal vector fields on a Randers manifold with certain curvature properties.In particular,we completely determine conformal vector fields on a Randers manifold of weakly isotropic flag curvature.
基金the National Natural Science Foundation of China (10371138)
文摘In this paper, we study a class of Finsler metrics defined by a vector field on a Riemannian space form. We give an explicit formula for those with isotropic S-curvature. This class contains all Randers metrics of constant flag curvature.
