Submanifolds of Manifolds with Structures

Abstract

This thesis comprises nine chapters. Chapter I is an introduction in nature and consists of basic definitions and results from geometry of lightlike hypersurfaces and lightlike submanifolds of indefinite almost complex and almost contact manifolds based upon exhaustive literature survey. Chapter II is devoted to the study of the geometry of lightlike hypersurfaces with parallel symmetric bilinear forms and semi-parallel lightlike hypersurfaces of indefinite cosymplectic manifold. The geometry of lightlike hypersurfaces and submanifolds of indefinite Kaehler manifold was studied by Duggal and Bejancu [56]. On the other hand, lightlike hypersurfaces of indefinite Sasakian manifolds were studied by Massambae [43. 44] and Kang et al. [98]. To study the lightlike geometry of hypersurfaces and submanifolds of a manifold, the second fundamental forms are important tools. When bilinear forms are parallel, it is more interesting to study the geometry of a manifold. In this chapter, it has been proved that if M is a lightlike ... newline