CR Submanifolds

Abstract

Let $\bar M$ be a complex m-dimensional (real 2m-dimensional) Kaehlerian manifold with almost complex structure J and with Kaehlerian metric g. Let M be a real n-dimensional Riemannian manifold isometrically immersed in $\bar M$. We denote by the same g the Riemannian metric tensor field induced on M from that of $\bar M$. The operator of covariant differentiation in $\bar M$ (resp. M) will be denoted by $\bar \nabla$ (resp. ▽).