Riemann submersiyonlarının geometrisi üzerine

Abstract

The first chapter of this thesis is devoted some basic topics, such as, Riemannian manifold, connection, curvatures, vector bundles and distributions. These terms are necessary for the other chapters of this thesis. In the second chapter, after the basic terminology, the fundamental tensor fields for a Riemannian submersion are given and their basic properties are studied. Afterwards geometric meaning of basic tensors are investigated. In the last chapter, firstly the covariant derivative of basic tensors are found and their basic properties are studied. Then the relation between two curvatures of Riemann manifolds are found by using these properties. KEYWORDS: Riemann submersion, basic tensor, covariant derivative, curvature, Ricci tensor, scalar curvature, distribution, vector bundle.