Ricci solitons on lightlike submanifolds

This study, prepared as a doctoral thesis, consists of four chapters. In the first chapter, which is given as an introduction, brief information about the literature on Ricci solitons and the general content of the thesis is given. In the second chapter, basic concepts about semi-Riemann manifolds, submanifolds and lightlike submanifolds of semi-Riemann manifolds are given to make the thesis understandable. In the third chapter, firstly, Ricci solitons on the lightlike hypersurface of a semi-Riemann manifold were examined with the help of the Rigged metric, and in this chapter, the potential vector field was taken as concurrent vector field and concircular vector field, and the necessary and sufficient conditions and characterizations were given for the existence of Ricci solitons on lightlike hypersurfaces and some theorems and results were obtained. In the last chapter, the fourth chapter, Ricci solitons were studied in their most general form on lightlike submanifolds. In this section, first Ricci solitons were studied on half lightlike and coisotropic submanifolds with additional dimension two, and characterizations were given by taking potential vector fields as special vector fields. In this last section, Ricci solitons on r-lightlike submanifolds were examined and characterizations were given in case potential vector fields are special vector fields (concurrent, concircular, etc.).