Some slant pseudo-Riemannian submersions in para-complex geometry

This thesis consists of five chapters. In the first chapter, the historical development of the subject is discussed. In the second chapter, the basic definitions regarding to the subjects in the next chapters are introduced. In the third chapter, semi-slant pseudo-Riemannian submersions from almost para-Hermitian manifolds to pseudo-Riemannian manifolds are defined and some geometric properties are obtained for all three types of angles in these submersions. These properties were also examined on the non-trivial examples. Also, the harmonicity and being totally geodesic of semi-slant pseudo-Riemannian submersions from almost para-Hermitian manifolds to pseudo-Riemannian manifolds are investigated. Then necessary and sufficient conditions for the maps to have totally geodesic fibers are obtained. Also, curvature properties for semi-slant pseudo-Riemannian submersions from para-Kaehler space forms are given. In the fourth chapter, hemi-slant pseudo-Riemannian submersions from almost para-Hermitian manifolds to pseudo-Riemannian manifolds are defined and some geometric properties are obtained for all three types of angles in these submersions. These properties were also examined on the non-trivial examples. Also, the harmonicity and being totally geodesic of hemi-slant pseudo-Riemannian submersions from almost para-Hermitian manifolds to pseudo-Riemannian manifolds are investigated. Then necessary and sufficient conditions for the maps to have totally geodesic fibers are obtained. Also, curvature properties for hemi-slant pseudo-Riemannian submersions from para-Kaehler space forms are given. In the fifth chapter, bi-slant pseudo-Riemannian submersions from almost para-Hermitian manifolds to pseudo-Riemannian manifolds are defined and some geometric properties are obtained for all three types of angles in these submersions. These properties were also examined on the non-trivial examples. Also, the harmonicity and being totally geodesic of bi-slant pseudo-Riemannian submersions from almost para-Hermitian manifolds to pseudo-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.