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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 $$\theta \neq 0$$ 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:
 53B25 Local submanifolds 53B35 Local differential geometry of Hermitian and Kählerian structures 53C40 Global submanifolds
Zbl 0716.53006