Different connections on almost contact metric manifolds

This thesis consists of four chapters. In the first chapter, basis notions and contact manifolds which we worked on later are mentioned. In the second chapter, in general meaning a new quarter symmetric non metric connection is defined and is given classification of this connection with respect to some specific conditions. Third chapter consists of two parts. In the first part,for n-dimensional Kenmotsu manifolds given with semi-symmetric metric connection, some curvature conditions are investigated. In the second part, Ricci soliton and gradient Ricci soliton notions are referred. Firstly, for 3-dimensional trans-Sasakian manifolds given with quarter symmetric non metric connection, Ricci soliton and gradient Ricci Ricci soliton notions are surveyed. Later same notions are studied for 3-dimensional normal almost contact metric manifolds given with quarter-symmetric metric connection. Last chapter is original part of our thesis and consists of two parts. In the first part, some curvature conditions are investigated and soliton concepts are taken for 3-dimensional quasi-Sasakian manifolds given with special defined quarter-symmetric non-metric connection. In the second part, soliton notions are dealed for 3-dimensional f-Kenmotsu manifolds with same connection.