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Generic submanifolds in almost Hermitian manifolds. (English) Zbl 0671.53040

A real submanifold M of an almost complex manifold \((M,J')\) is called a generic submanifold if dim J\({}'T_ xM\cap T_ xM\) is constant on M. In this article, the author proves that a generic submanifold of a complex manifold is a CR-manifold. She studies sufficient conditions for a real submanifold in a Kähler manifold to be generic. Several results concerning the canonical distributions of a generic submanifold in a Kähler manifold are also obtained.
Reviewer: B.Y.Chen

MSC:

53C40 Global submanifolds
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