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Semi-slant submanifolds of a Kaehlerian manifold. (English) Zbl 0847.53012
The author defines a semi-slant submanifold M of a Kählerian manifold to be a submanifold whose tangent bundle is the direct sum of a complex distribution and a slant distribution with the slant angle θ0 in the sense of [the reviewer, Geometry of slant submanifolds. Leuven: Kath. Univ. Leuven, Dept. of Mathematics. 123 p. (1990; Zbl 0716.53006)]. The author obtains the necessary and sufficient conditions for the complex and slant distributions to be integrable. He also obtains a necessary and sufficient condition for a semi-slant submanifold to be the Riemannian product of a complex submanifold and a slant submanifold.

MSC:
53B25Local submanifolds
53B35Hermitian and Kählerian structures (local differential geometry)
53C40Global submanifolds (differential geometry)