复射影空间中拟全实极小子流形

摘要

The authors studied the relations between the curvature and geometric feature of quasi-totally real minimal submanifold in a complex projective space CP(n+p)/2. With the help of moving-frame method and Bochner skills, somerigidity theorems on sectional curvature and Ricci curvature were obtained. The authors have proved that if the sectional curvature of Mn is not less than (n + 3 )/[ 2 (n + 1 ) ] or Ricei curvature is not less than n + 1 -3p/n + 12p/n2(n≥4) or 3/4n +2(n≤4), then p=n,M=RPn.%运用活动标架法和Bochner技巧,研究复射影空间CP(n+p)/2中拟全实极小子流形曲率与几何特征的关系,得到了截面曲率和Ricci曲率的刚性定理.证明了:若Mn的截面曲率处处不小于n+3/2(n+1)或Ricci曲率处处不小于n+1-3p/n+12p/n2(n≥4),3/4n+2(n≤4),则p=n,M=RPn.