Contact -product of a trans-Sasakian manifold

Abstract

We obtain a necessary and sufficient condition for a -submanifold of a trans-Sasakian manifold to be contact -product in terms of fundamental tensor of Weingarten with respect to the normal section as well as to the canonical structure. We have also obtained some results on - submanifolds of 𝛼-Sasakian and 𝛽-Kenmotsu manifolds.