伪黎曼空间型中具有常数量曲率类空子流形

Space-like submanifolds with constant scalar curvature in a Pseudo-Riemanian space form

研究了伪黎曼空间型中具有常数量曲率的类空子流形,通过构造一个自共轭的微分算子,建立了该微分算子与第二基本形式模长平方的拉普拉斯之间的关系;讨论了该类子流形的一些性质,获得了使此子流形成为全脐子流形的一个条件;得到了关于第二基本形式模长平方的一个积分不等式.

Space-like submanifolds with constant scalar curvature in a Pseudo-Riemannian space form was studied. By the structure of a new differential operator, it was estabilished a relation between the operator and the Laplace of S. The properties of this kind of submanifolds were discussed. A condition which would make this kind of submanifolds toally umbilical was given and an integral inequality in respect of S was obtained.