On the geometry of contact riemannian submersions

This study, which was prepared as a master's thesis, consists of five main parts. In the first chapter, after the introduction to the subject, the problems discussed in this thesis are given. In the second part, information was given about the historical development of the subject. In the third chapter, general information about Riemannian manifolds, submanifolds and contact manifolds were expressed by giving place to the basic definitions and theorems related to the subject. In the fourth chapter, firstly, some basic concepts about Riemannian submersions are given. Some notions about sectional curvature, Ricci tensor and scalar curvature on the total manifold of these submersions are presented. Then, general information about contact Riemannian submersions defined between almost contact Riemannian manifolds is given. Finally, some inequalities about contact Riemann submersions have been established. Some necessary and sufficient conditions were determined for the equality of these inequalities. In the last part, some results obtained from this thesis study are presented and some suggestions about the subject are given.