On the anti invariantriemann submersions

In this thesis, the basic properties of anti-invariant Riemann submersions are expressed. The basic properties of anti-invariant Riemannian submersions defined from (2n-1)-dimensional Hermitian manifold to a (2n-1)-dimensional Riemannian manifold were investigated, and the actions of almost complex J structure on these submersions were investigated. The first chapter of this thesis, which consists of five chapters, is reserved for the introduction. In the second chapter, some basic concepts, definitions and theorems used in other chapters are presented and some basic information about complex manifolds are given. In the third chapter, firstly, general concepts about Riemannian submersions, Riemann curvature tensor field on submersions and the basic properties anti-invariant Riemannian submersions are presented. In the fourth chapter, contact type anti-invariant Riemann submersions are introduced and some basic equations are given. In the fifth chapter, some conclusions and suggestions are given with the help of relations obtained in the fourth chapter.