摘要
本文利用第二基本形式的长度平方和平均曲率的关系研究常曲率空间中具平行平均曲率向量的子流形为全脐的ｐｉｎｃｈｉｎｇ问题，获得了一定条件下的最佳ｐｉｎｃｈｉｎｇ区间，并确定了ｐｈｉｎｃｎｉｎｇ区间端点处对应非全脐子流形的分类．
We discuss the pinching problem for a submanifold with parallel mean curvature vector in spaces of constant curvature to be totally umbilical by using the relationship between the square of the length of the second fUndamental form and the mean curvature, we obtain the best pinching intervals and give a complete classification of submanifolds at the terminal of the intervals.
基金
河南省自然科学基金
