  We prove that under certain conditions on the mean curvature and on the
Kaehler angles, a compact submanifold M of real dimension 2n, immersed into a
Kaehler-Einstein manifold N of complex dimension 2n, must be either a complex
or a Lagrangian submanifold of N, or have constant Kaehler angle, depending on
n=1, n=2, or n \geq 3, and the sign of the scalar curvature of N. These results
generalize to non-minimal submanifolds some known results for minimal
submanifolds. Our main tool is a Bochner-type technique involving a formula on
the Laplacian of a symmetric function on the Kaehler angles and the
Weitzenboeck formula for the Kaehler form of N restricted to M.
