空间形式S^n＋p（c）中法丛平坦的常数量曲率子流形

Submanifolds with Flat Normal Bundle and Constant Scalar Curvature in Space Form S~(n+p) (c)

得到空间形式S^n+p(c)中法丛平坦的常数量曲率子流形的一个刚性定理：设M^n(n≥3)是空间形式S^n+p(c)中标准平均曲率向量平行的紧致子流形和M^n的标准数量曲率R为常数．若法丛N(M^n)平坦且(1)R-c≥0，(2)M^n的截面曲率K>0，则M^n是S^n+p(c)中的全脐子流形。

In this paper the author obtains a rigid result for submanifolds with flat normal bundle and constant scalar curvature in the space form S~(n+p)(c) :Let M~n( n ≥ 3) be a submanifold with parallel normalized mean curvature vector field immersed in the space form S~(n+P)(c) .Suppose that the normalized scalar curvature R is constant and R - c ≥ 0 . If the normal bundle N(M~n) is fiat and K > 0 ,then M~n is totally umbilical in S~(n+p)(c) .