Biharmonic submanifolds of Para-Sasakian manifolds

This study, which is designed as a master thesis, consists of five chapters. The first chapter is the introduction part and this section presents information on the emergence and development of biharmonic maps and almost paracontact metric manifolds. The second section is devoted to some basic concepts for better understanding of the rest of the thesis. In the third section we give semi-Riemannian manifolds, some special operators, almost paracontact metric manifolds and biharmonic submanifolds. The fourth chapter is the orginal part of this thesis. Firstly, we investigate biharmonicity conditions for a spacelike or timelike Legendre curve on a 3-dimensional para-Sasakian manifold. Then we obtain necessary and sufficient conditions for a hypersurface of para-Sasakian manifolds admitting the characteristic vector field in the tangent and the normal bundle respectively to be biharmonic. The fifth section is divided into results and recommendations. Key Words: Biharmonic curves; Biharmonic hypersurfaces; Almost paracontact metric manifolds; Para-Sasakian manifolds.