Totally umbilicalCR-submanifolds of Semi-Riemannian Kaehler manifolds

摘要

We study totally umbilicalCR-submanifolds of a Kaehler manifold carrying a semi-Riemannian metric. It is shown that for dimension of the totally real distribution greater than one, these submanifolds are locally decomposable into a complex and a totally real submanifold of the Kaehler manifold. For dimension equal to one, we show, in particular, that they are endowed with a normal contact metric structure if and only if the second fundamental form is parallel.