摘要
In this paper, we continue to discuss the sufficient conditions for a compact Kaehler submanifold in a locally symmetric Bochner-Kaehler manifold to be totally geodesic. We have obtained the following results. Theorem 1. Let M^(n+p) be a locally symmetric Bochner-Kaehler manifold of complex dimensions n+p and M^n a compact Kaehler submanifold of complex dimension (n≥2) in M^(n+p). Let and, where Ric(M)_x denotes the Ricci curvature of M^(n+p) at the point x. If the scalar curvature ρ_M of M^n satisfies then M^n must be totally geodesic in M^(n+p). Theorem 2. Let M^n and M^(n+p) be the same as those in Theorem 1. If the Ricci curvature Q_M of M^n satisfies then M^n is totally geodesic in M^(n+p).
