摘要
本文研究爱因斯坦黎曼流形的全脐超曲面,给出它为全测地的或常曲率的充分条件。也研究全测地超曲面。
The main result obtained in the present paper is that: Let M be a totally umbilical hypersurface in an Einstein Riemannian manifold N. If the conformal curvature tensor (?) of N satisfies the relation (?)_T(?)=ω(T)(?), where T is any vector field on M and ω is a 1-form, then M either is of constant curvature or is totally geodesic. This paper also discusses the totally geodesic hypersurfaces in some Einstein Riemannian manifolds.
基金
江西省自然科学基金
关键词
爱因斯坦流形
超曲面
全脐
全测地
Einstein manifold, hypersurface, umbilical, totally geodesic, curvature
