On scalar curvature for totally real minimal submanifolds in CP n

Let CP~n be a complex projective n-space with the Fubini-Study metric of constantholomorphic sectional curvature c,and M be an n-dimensional compact totally real minimalsubmanifold in CP~n. It is known from refs. [1-3] that if the scalar curvature ρ≥n~2(n-2)c/2(2n-1) for M, then M is either totally geodesic in CP~n or n=2 and ρ=0, and M is a finiteRiemannian covering of the unique flat torus minimally imbedded in CP~2 with the parallel