Sectional curvature of Kähler submanifolds of a complex projective space (Q1109352)

The main purpose of this paper is to prove the following theorem: Let M n (n\(\geq 2)\) be a complete Kähler submanifold of complex dimension n, immersed in the complex projective space \({\mathbb{C}}P\) m(1). Let K be the sectional curvature of M n. Then \(K\geq 1/8\) if and only if M n is an imbedded submanifold congruent to the standard imbedding of \({\mathbb{C}}P\) n(1) or \({\mathbb{C}}P\) n(\()\). The same result was obtained independently by A. Ros using another method. Let us mention that this result is a generalization of K. Ogiue's conjecture resolved by A. Ros and L. Verstraelen.