常曲率黎曼空间中的可展子流形

THE DEVELOPABLE SUBMANIFOLDS IN RIEMANNIAN SPACES OF CONSTANT CURVATURE

本文就常曲率空间S^m的可展子流形M^z=∞~1S^(n-1)证得若干结果,主要是:对任一n(1〈n〈m),S^m中可展子M^z的变形依赖于决定一条曲线的m-1个单参数的任意函数。

In this paper, we prove some results on the developable submanifold M = S-xin the space S'of constant curvature. The main one is as follows.For any n(l<n<m),the deformation of of the developable submnifold M in S' depents on (m- 1 ) arbitrary functions of one-parameter, by them a curve is detrmined in Sm.