论文摘要
本文主要讨论局部对称Lorentz空间中具有常平均曲率、常数量曲率的两类类空超曲面,通过估计两种情形下超曲面的第二基本形式模长平方S的Laplace,利用Yau的极大值原理,获得了这些超曲面是全脐的一些充分条件.论文共分为三节.第一节介绍局部对称Lorentz空间中类空超曲面的基本公式和初步计算.第二节主要讨论局部对称Lorentz空间中具有常数量曲率的类空超曲面Mn,获得了关于Mn的第二基本形式模长平方S的两个间隙定理,具体见定理2.1和定理2.2 .第三节研究局部对称Lorentz空间中具有常平均曲率的类空超曲面,证明了当Mn的第二基本形式模长平方S满足适当的上界时, Mn是全脐超曲面(定理3.1 ),同时获得了当Mn具有非负截面曲率时的一个刚性定理(定理3.2 ).
论文目录
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