关于Weingarten超曲面的一个存在性定理

AN EXISTENCE THEOREM OF WEINGARTEN HYPERSURFACES

本文研究伪黎曼空间型中一类特殊的Weingarten超曲面的存在性问题.通过引入伪黎曼空间型中旋转超曲面的概念,并给出其主曲率计算公式,得到伪黎曼空间型中旋转型Weingarten超曲面的存在性定理.推广并统一了相关结果.

A special kind of existence problem of Weingarten hypersurfaces in pseudo-Riemannian space form is investigated in this paper, By introducing the concept of rotation hypersurfaces in pseudo-Riemannian space form and computing their principal curvatures, we obtain the existence theorem of rotation Weingarten hypersurfaces in pseudo-Riemannian space form. The relevant results are extended and unified.