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
1 Introduction Let （M, g） be a compact and connected Riemannian manifold. The Laplace operator △ on functions on M has a discrete spectrum Spec（M, g）= {0=λ<sub>0</sub>【λ<sub>1</sub>≤λ...1 Introduction Let （M, g） be a compact and connected Riemannian manifold. The Laplace operator △ on functions on M has a discrete spectrum Spec（M, g）= {0=λ<sub>0</sub>【λ<sub>1</sub>≤λ<sub>2</sub>≤…}. We say that two Riemannian manifolds （M, g）展开更多
A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved.If there holds the following condition：integral（sk（x0,s）ds= o...A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved.If there holds the following condition：integral（sk（x0,s）ds= o（log r）） from n=0 to r then the manifold is flat.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
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].
基金Project supported by the Natural Science Foundation of Jiangxi Province
文摘1 Introduction Let （M, g） be a compact and connected Riemannian manifold. The Laplace operator △ on functions on M has a discrete spectrum Spec（M, g）= {0=λ<sub>0</sub>【λ<sub>1</sub>≤λ<sub>2</sub>≤…}. We say that two Riemannian manifolds （M, g）
基金Supported by the National Natural Science Foundation of China (Grant No.70631003)the Natural Science Foundation of Anhui Education Department (Grant No.KJ2011A061)+1 种基金the Natural Science Foundation of Anhui Science and Technology Department (Grant No.1104606M01)the Doctor of Philosophy Foundation of Anhui University of Architecture (Grant No.2007-6-3)
文摘A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is proved.If there holds the following condition：integral（sk（x0,s）ds= o（log r）） from n=0 to r then the manifold is flat.
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.
