局部对称伪黎曼δ-拼挤流形中的极大类空子流形

Maximal Space-like Submanifolds in Locally Symmetric δ-pinched Pseudo-Riemannian Submanifolds

在子流形几何中,极小子流形的研究是一个热门课题,许多作者做了研究.伪黎曼流形在物理和数学上都具有重要的研究价值,自然伪黎曼流形中的极大子流形就成了大家所关注的对象.局部对称伪黎曼流形是伪黎曼空间型的推广.主要研究了局部对称伪黎曼δ-拼挤流形中的极大类空子流形,通过活动标架法对子流形的第二基本形式模长平方的Laplacian进行了计算,从而得到了这类子流形是全测地子流形的一个充分条件,推广了局部对称空间中全测地子流形的外围空间.

In the geometry of the submanifolds,the study of minimal submanifolds is a hot topic,and many authors have done a lot of research.Pseudo-Riemannian manifold has an important research value in physics and mathematics,naturally,maximal manifold in it has become the object that we are concerned about.The locally symmetric pseudo-Riemannian manifold is a generalization of the pseudo-Riemannian space type.In this paper,we mainly investigate the maximal space-like submanifolds in locally symmetric 5-pinched pseudo-Riemannian manifolds.By calculating the Laplacian about the square of the second fundamental form of submanifolds with the active frame method,we obtain a sufficient condition for this kind of submanifolds to be totally geodesic,which generalize and improve the outer space of totally geodesic in an iocally symmetric space.