欧氏空间中的相互平行子流形

Paraller Submanifolds in Euclidean Space

对欧氏空间中的子流形Ｍ，若其法联络平坦，则存在平行的法向量场，由此可得与Ｍ平行的子流形Ｍ。给出了相互平行子流形Ｍ和Ｍ的曲率之间的关系及一些不变性质。

Let M be a Submanifold of Euclidean space with flat normal connection, then there exist parallel normal vector fields. We can define a submanifold M in parallel with M. In this paper, we obtain the relationship of curvature between M and M, and some invariant property.