CR submanifolds of Hermitian manifolds and the tangential CR equations

We exhibit the relationship between the second fundamental form and the Levi form of a CR submanifold M (in the sense of A. Bejancu, [5]) in a Hermitian (e.g., Kählerian or locally conformal Kähler) manifold M^{2N} and start a study of the CR extension problem from M to M^{2N}