The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method...The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method is completely different. Meanwhile,we get better conclusion than that of [3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan[4].展开更多
In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized.
In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theo...In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theorems reduce to the theorems of[1],[2].展开更多
Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we ge...Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold.展开更多
The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We firs...The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.展开更多
In this paper we obtain some formulas for totally umbilical submanifolds in a localiy symmetric manifold, and dcrivc some local rcsults on the submanifolds from these formulas.
In our preceding paper, we gave some Pinching conditions of sectional curvature and holomorphic sectional curvature for a compact Kaehler submanifold Mn in a locally symmetric Bochner-Kaehler manifold （?）n+p to be t...In our preceding paper, we gave some Pinching conditions of sectional curvature and holomorphic sectional curvature for a compact Kaehler submanifold Mn in a locally symmetric Bochner-Kaehler manifold （?）n+p to be totally geodesic. As a continuation, this letter gives the Pinching conditions of Ricci curvature and scalar curvature for Mn in （?）n+p to be totally geodesic. The main results are as follows.展开更多
This paper gives some sufficient conditions for a compact Kaehler submanifold M<sup>n</sup> in a locally symmetric Bochner-Kaehler manifold <sup>n+p</sup> to be totally geodesic. The conditions...This paper gives some sufficient conditions for a compact Kaehler submanifold M<sup>n</sup> in a locally symmetric Bochner-Kaehler manifold <sup>n+p</sup> to be totally geodesic. The conditions are given by inequalities which are established between. the sectional curvature（resp, holomorphic sectional curvature） of M<sup>n</sup> and the Ricci curvature of <sup>n+p</sup>. In particular, similar results in the case where <sup>n+p</sup> is a complex projective spathe are contained.展开更多
文摘The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method is completely different. Meanwhile,we get better conclusion than that of [3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan[4].
文摘In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized.
文摘In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theorems reduce to the theorems of[1],[2].
文摘Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold.
文摘The purpose of this paper is to study complete space-like submanifolds with parallel mean curvature vector and flat normal bundle in a locally symmetric semi-defnite space satisfying some curvature conditions. We first give an optimal estimate of the Laplacian of the squared norm of the second fundamental form for such submanifold. Furthermore, the totally umbilical submanifolds are characterized.
文摘In this paper we obtain some formulas for totally umbilical submanifolds in a localiy symmetric manifold, and dcrivc some local rcsults on the submanifolds from these formulas.
文摘In our preceding paper, we gave some Pinching conditions of sectional curvature and holomorphic sectional curvature for a compact Kaehler submanifold Mn in a locally symmetric Bochner-Kaehler manifold （?）n+p to be totally geodesic. As a continuation, this letter gives the Pinching conditions of Ricci curvature and scalar curvature for Mn in （?）n+p to be totally geodesic. The main results are as follows.
文摘This paper gives some sufficient conditions for a compact Kaehler submanifold M<sup>n</sup> in a locally symmetric Bochner-Kaehler manifold <sup>n+p</sup> to be totally geodesic. The conditions are given by inequalities which are established between. the sectional curvature（resp, holomorphic sectional curvature） of M<sup>n</sup> and the Ricci curvature of <sup>n+p</sup>. In particular, similar results in the case where <sup>n+p</sup> is a complex projective spathe are contained.
