关键词: 复射影空间, 一般子流形, 极小子流形, 拟全实子流形

Abstract:

The authors studied the relations between the curvature and geometric feature of quasitotally real minimal submanifold in a complex p
rojective space CP^(n+p)/2. With the help of movingframe method and Bochner skills, some rigidity 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 Ricci curvature is not less than n+1-3p/n+12p/n²(n≥4) or 3n/4+2(n≤4), then p=n, M=RPⁿ.

Key words: complex projective space, generic submanifold, minimal submanifold, quasitotally real submanifold