Riemannian Submersions and Planar Normal Sections
Project no. 479 · Status: Kapanmış · 2017
Summary
This thesis essentially consists of four chapters. In the first chapter, the informations related to the emergence process and developments in the literature of the submersions, Riemannian submersions, planar normal sections, anti-invariant Riemannian submersions and complex manifolds are presented. Furthermore, the contents of the problems discussed in this thesis are briefly mentioned. In the second chapter, basic definitions, theorems and related notions used throughout the thesis are given. In the third chapter, first the definition of pointwise k-planar normal section is reminded and under the light of this definition, pointwise k-planar horizontal section along the Riemannian submersions is defined. After that the classifications and characterizations about this definition are obtained. Finally, geometric meanings of submersions with pointwise k-planar horizontal section are given. In the fourth chapter, first anti-invariant Riemannian submersion from Kahler manifolds onto a Riemannian manifold with totally umbilical fibers is defined and characterizations for this kind of maps are obtained. After that new results in terms of O'Neill tensor fields are given. Besides this, concept of anti-invariant Riemannian submersions from complex spaces onto a Riemannian manifold is studied.