This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-...This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.展开更多
Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. ...Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.展开更多
In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finall...In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.展开更多
Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn＋p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem ...Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn＋p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results.展开更多
In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic subman...In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.展开更多
Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame f...Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.展开更多
Let CP^n be a complex projective n-space with the Fubini-Study metric of constantholomorphic sectional curvature c,and M be an n-dimensional compact totally real minimalsubmanifold in CP^n. It is known from refs. [1-3...Let CP^n be a complex projective n-space with the Fubini-Study metric of constantholomorphic sectional curvature c,and M be an n-dimensional compact totally real minimalsubmanifold in CP^n. It is known from refs. [1-3] that if the scalar curvature ρ≥n^2(n-2)c/2(2n-1) for M, then M is either totally geodesic in CP^n or n=2 and ρ=0, and M is a finiteRiemannian covering of the unique flat torus minimally imbedded in CP^2 with the展开更多
Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as foll...Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=zz-t＋O（3）,where W ={wij}1≤ i,j≤ m and Z ={Zij}1≤i≤ m,1≤j≤N We prove that M is biholomorphically equiva-lent to the model W =zz-tif and only if is formally equivalent to it.展开更多
基金the Natural Science Foundation of Education Committee of Anhui Province(2004kj166zd)Foundation for Younger Teachers of Anhui Normal University(2005xqn01).
文摘This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.
文摘Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
文摘In this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.
基金Supported by the Natural Science Foundation of Anhui Educational Committee (Grant No. KJ2011Z149)
文摘Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn＋p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results.
基金Research partially supported by the Ministry of Science and Environmental Protectipn of Serbia, Project 1646Research partially supported by EGIDE, Pavle Savic 07945VC(France)
文摘In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derive a pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of the totally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.
基金Foundation item： the Natural Science Foundation of Anhui Educational Committee （No. KJ2008A05ZC） the Younger Teachers of Anhui Normal University （No. 2005xqn01）.
文摘Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.
基金Project supported by the National Natural Science Foundation of China and the Science Foundation of Zhejiang Province.
文摘Let CP^n be a complex projective n-space with the Fubini-Study metric of constantholomorphic sectional curvature c,and M be an n-dimensional compact totally real minimalsubmanifold in CP^n. It is known from refs. [1-3] that if the scalar curvature ρ≥n^2(n-2)c/2(2n-1) for M, then M is either totally geodesic in CP^n or n=2 and ρ=0, and M is a finiteRiemannian covering of the unique flat torus minimally imbedded in CP^2 with the
文摘Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=zz-t＋O（3）,where W ={wij}1≤ i,j≤ m and Z ={Zij}1≤i≤ m,1≤j≤N We prove that M is biholomorphically equiva-lent to the model W =zz-tif and only if is formally equivalent to it.
基金Supported by the National Natural Science Foundation of China(11071005)Foundation for Excellent Young Talents of Higher Education(2011SQRL021ZD)+1 种基金the Natural Science Foundation of Anhui Educational Committee(KJ2010A125)the Natural Science Foundation of Anhui Educational Committee(KJ2012b197)
