The author defines a semi-slant submanifold
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
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.