<正> Let M~n be a compact Kaehler submanifold of complex dimension n immersed in the complex projective space CPm(1) endowed with the Fubini-Study metric of constant holomorphic sectional curvature 1. Let Q and r denote the Ricci curvature and the scalar curvature of M~n respectively. (i) K. Ogiue proved that if Q>n/2, then M~n is totally