Hilbert空间的平行PF子流形

Paraller PF Submanifolds of Hilbert Space

对于 Hilbert空间的 PF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.本文讨论了 M与 M 的曲率之间的关系及不变性质 .

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