Semi-invariant Submanifolds

The present text, Semi-invariant Submanifolds is devoted to the study of semi-invariant submanifolds of manifold equipped with certain distinguished structures and connections. The structures such as Sasakian, trans Sasakian, Kenmotsu manifold is one of the most interesting topic in the differential geometry of the manifolds. In a manifold with an almost contact metric structure, the (1, 1) structure vector field transforms a vector into a vector perpendicular to it. Thus it becomes a natural motivation to study submanifold of a manifold with almost contact metric structure, according to the behavior of its tangent bundle under the action of the (1, 1) structure vector field of the ambient manifold. There are two well known classes of submanifolds, namely invariant submanifolds and anti-invariant submanifolds. In the first case the tangent spaces of the sub-manifolds remains invariant under the action of the (1, 1) structure tensor field, whereas in the second case it is mapped into the normal space.