The nondegenerate affine locally symmetric surfaces in R^4 with the transversal bundle defined by Nomizu and Vrancken have been studied and a complete classification of the locally symmetric surfaces with flat normal ...The nondegenerate affine locally symmetric surfaces in R^4 with the transversal bundle defined by Nomizu and Vrancken have been studied and a complete classification of the locally symmetric surfaces with flat normal bundle has been given.展开更多
Let M^n be a compact Willmore submanifold in the unit sphere Sn＋p. In this note, we investigate the first eigenvalue of the SchrSdinger operator L = -△ - q on M, where q is some potential function on M, and present...Let M^n be a compact Willmore submanifold in the unit sphere Sn＋p. In this note, we investigate the first eigenvalue of the SchrSdinger operator L = -△ - q on M, where q is some potential function on M, and present a gap estimate for the first eigenvalue of L.展开更多
It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（...It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.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
A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.
The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains a...The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.展开更多
文摘The nondegenerate affine locally symmetric surfaces in R^4 with the transversal bundle defined by Nomizu and Vrancken have been studied and a complete classification of the locally symmetric surfaces with flat normal bundle has been given.
基金Supported by the National Natural Science Foundation of China(11071211)the Zhejiang Natural Science Foundation of China
文摘Let M^n be a compact Willmore submanifold in the unit sphere Sn＋p. In this note, we investigate the first eigenvalue of the SchrSdinger operator L = -△ - q on M, where q is some potential function on M, and present a gap estimate for the first eigenvalue of L.
基金Research supported by the National Natural Science Foundation of China(10771187)Trans-Century Training Programme Foundation for Talents by the Ministry of Education of China.
文摘It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.
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A class of twisted special Lagrangian submanifolds in T＊R^n and a kind of austere submanifold from conormal bundle of minimal surface of R^3 are constructed.
基金Project supported by the Spanish Ministry of Science and Technology Grants MTM2005-O8689-G02-02 and MTM 2004-06015-C02-01.
文摘The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.
