Riemannian submersions and planar normal sections

This thesis essentially consists of four chapters. In the fi rst 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 defi nitions, theorems and related notions used throughout the thesis are given. In the third chapter, first the defi nition 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 defi ned. After that the classifi cations and characterizations about this defi nition 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 fi bers is defi ned and characterizations for this kind of maps are obtained. After that new results in terms of O'Neill tensor elds are given. Besides this, concept of anti-invariant Riemannian submersions from complex spaces onto a Riemannian manifold is studied.