Complete Totally Real Submanifolds with Parallel Mean Curvature

i. Introduction A submanifold M in a Kaehler manifold M is said to be totally real if every tangent space of M is mapped into its normal space by the complex structure of M. Some fundamental properties of totally real submanifolds can be found in [1], [2]. Let σ be the second fundamental form of M. The mean curvature η of M is defined by η=tr σ , and M is called a submanifold with