S^m+p中子流形上的一个不等式

An Inequality on the Submanifolds of S^m+p

摘要: 设x:M^m→S^m+p(m≥2; p≥2)是m+p维单位球S^m+p中的一个m维无脐点子流形，M^m上的MO^¨bius第二基本形式B是M^m在S^m+p中的MO^¨bius变换群下的不变量，本文得到不等式，证明了等号成立的条件。

Abstract: Let x:M^m→S^m+p(m≥2; p≥2) be an m-dimensional no umbilical submaniods in m+p-dimensional unit sphere S^m+p. The MO^¨bius second basic from B of M^m is the invariant of under the group of MO^¨bius transformations in S^m+p. We obtain inequality . The conditions for the equality sign are proved.