【作者】 武爱菊；

【导师】 纪永强；

【作者基本信息】 宁夏大学 ， 基础数学， 2004， 硕士

【摘要】 本论文讨论了四种黎曼流形中有关pinching问题包括以下四个方面的内容： 1．研究了拟常曲率黎曼流形中的极小子流形，得到了积分不等式从而得到拟常曲率空间的极小子流形是全测地子流形的四个平行条件。 2．讨论N_p^n+p局部对称的伪黎曼流形，它的截面曲率K_N，C₁≤K_N≤C₂．Mⁿ是N_p^n+p的类空子流形，通过对于Mⁿ的第二基本形式模长平方的估计，得到是全测地子流形。 3．研究了De Sitter空间中具有单位平行平均曲率向量的紧致类空子流形位于一个全测地子流形的一个充分条件。 4．讨论常曲率空间具有平行中曲率向量子流形，并减弱条件为紧致伪脐得到是全脐子流形的较好结果。更多还原

【Abstract】 The paper describes some pinching problems about four species sub manifolds in Rieman manifold.1 Many questions of compact minimal sub manifolds in Riemanian manifold with quasi-constant curvature are studied. When it is total geodesic riemannia sub manifold. Four integrating adequate conditions are given.2 Le Npn+p be a locally symmetric complete and connected pseudo-Riemanian manifold whose sectional curvature kN satieties c1 kN c2 let M"be a maximal space like sub manifold in Npn+p, An.estimate is given for the square of the length of the second fundamental form of Mn. It is total geodesic sub manifold .3 The pinching problems are discussed on the compact space-like sub manifold with unit parallel mean curvature vector in de sitter space a sufficient condition for it to be total geodesic sub manifold.4 A compact sub manifold with positive curvature in the constant curved manifold s weaken the condition s of the theorems and obtained better conclusion for it to be a totally umbilical sub manifold.更多还原