Abstract
In the present paper, we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if A(xi) = 0; and the submanifold will be skew semi-invariant submanifold if del w=0. The equivalence relations for the skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant xi(perpendicular to)-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is CR-manifold. An example of dimension 5 is given to show that a skew semi-invariant xi(perpendicular to) submanifold is a CR-structure on the manifold.