CR relatives Kaehler manifolds

Abstract

In this paper we show that two Kähler manifolds which do not share a Kähler submanifold, do not share either a Levi degenerate CR-submanifold with constant dimension Levi kernel. In particular, they do not share a CR-product. Further, we obtain that a Levi degenerate CR-submanifold of ${\mathbb{C}}^n$ cannot be isometrically immersed into a flag manifold.

8 pages. In the second version an inaccuracy in the proof of Corollary 2 has been corrected

References in corpus (1)

• A bounded homogeneous domain and a projective manifold are not relatives