In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.
The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.展开更多
The author obtains some theorems for a function to be the scalar curvature of some complete conformal metric of a noncompact complete Riemann manifold, and also presents a kind of manifolds oil which Yamabe problem is...The author obtains some theorems for a function to be the scalar curvature of some complete conformal metric of a noncompact complete Riemann manifold, and also presents a kind of manifolds oil which Yamabe problem is unsolvable.展开更多
文摘In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.
基金Supported by the National Fundations of Natural sciences. Supported by the Henan Fundations of Scientific Committee.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.
文摘The author obtains some theorems for a function to be the scalar curvature of some complete conformal metric of a noncompact complete Riemann manifold, and also presents a kind of manifolds oil which Yamabe problem is unsolvable.
