PINCHING THEOREMS FOR TOTALLY REAL MINIMAL SUBMANIFOLDS IN CP n

摘要

Let M be an n-dimensional totally real minimal submanifold in CPnn.nWe prove that ifM is semi-parallel and the scalar curvature τ ,n−(n−1)(n−2)(n+1)n2n≤ τ ≤ 0,nthen M is an open part of the Clifford torus Tnn⊂ CPnn.If M is semi-parallel and thenscalar curvature τ , n(n − 1) ≤ τ ≤ n3n−3n+2n2n, thenMis an open part of the real projectivenspace RPnn.