Abstract
In this paper, first, we find the integrability theorems for the invariant and slant distributions which appeared in the concept of semi-slant submanifolds. Utilizing these theorems, we prove that a semi-slant submanifold reduces to be a warped product semi-slant submanifold, provided some necessary and sufficient conditions concerning the shape operators. Also, it is shown that a few earlier results are exceptional cases of this paper results.
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