Sasaki空间形式^(2n+1)(c)中极小积分子流形

Minimal Integral Submanifolds of Sasakian Space Form

设 M2n+1(c)是2n+1维常φ 截面曲率c的Sasaki空间形式,Mn是 M2n+1(c)(c>-3)的n维紧致极小积分子流形、S.Maeda(TensorNS,1981,35:200～204.)证明了:当n 5时,若M的Ricci曲率满足Ric(Mn)>(n-2-14,n)·c+3则Mn是全测地的.讨论了n=4的情形,得到类似的结果.

Let ^(2n+1)(c) denote a (2n+1) dimensional Sasakian space form of contact φ-sectional curvature C, M^n be a n-dimensional compact minimal integral submanifolds of ^(2n+1)(c). S. Meada (Tensor N S,1981,35:200～204.) proved that if Ric (M^n)>(n-2-1n)·c+34,n≥5, then M^n is totally geodesic. The purpose of the present paper is to obtain the analogous results for the case where n=4.