Geometry of slant submersions

This work consists of four chapters. The first chapter is devoted presentation of the problems and their background. In the second chapter, preliminaries, some necessary definitions, lemmas and theorems that will be needed for later use are given. In the third chapter, the concept of pointwise slant submersion from almost product Riemannian manifolds onto Riemannian manifolds is defined and is investigated with an example. Also, the harmonicity and totally geodesic of pointwise slant submersion from local product Riemannian manifolds onto Riemannian manifolds are investigated. Then necessary and sufficient conditions for the maps to have totally geodesic fibers are obtained. Also, the curvature relations between the total manifold and the base manifold for such submersions are given. In the four chapter, pointwise slant submersion from almost contact metric manifolds onto Riemannian manifolds is defined and examples are given. Also, the harmonicity of pointwise slant submersion from cosymplectic manifolds onto Riemannian manifolds according to the state to be vertical or horizontal of characteristic vector field is investigated and necessary and sufficient conditions for the maps to have totally geodesic fibers are given. Then, the curvature relations between the total manifold and the base manifold for such submersions according to the state to be vertical or horizontal of characteristic vector field are obtained. Keywords: Riemannian Submersion, Almost Product Riemannian Manifold, Almost Contact Metric Manifold, Cosymplectic Manifold, Pointwise Slant Submersion.