Geometry 0f Bi-slant submanifolds

During my Ph.D certain aspects of submanifolds theory in the setting of complex as well as contact manifolds has been studied, in my thesis we have extended several results of submanifolds theory in more general settings. The setting of trans-Sasakian manifolds in a way unifies the two classes of manifolds namely Sasakian manifold and other Kenmotsu manifold. By studying submanifolds of a trans-Sasakian manifold, one clearly finds out the deviations in the geometric behavior of submanifold in Sasakian and kenmotsu manifolds. With this motivation we have studied slant and semi-slant submanifolds of trans-Sasakian manifold and obtained a criterion for existence of slant submanifold in a trans-Sasakian manifold. Pseudo-slant submanifold is a special case of bi-slant submanifold, we describe a method of constructing pseudo-slant submanifold in an almost contact manifold. Moreover, a formula for covariant derivative of the endomorphism T is established which ensures the existence of a pseudo-slant submanifold of a sasakian manifold. Next, we also obtained a classification of totally umbilical semi-invariant submanifolds of a nearly trans-Sasakian manifold.