Generalized biharmonic Riemannian submersions

This study consists of eight chapters. In the first chapter, which is organized as an introduction chapter, information about the emergence and development of Riemann submersions, harmonic maps, biharmonic maps and the generalizations of these maps are presented. In the second chapter, a literature summary is given according to the purpose of the study. In the third chapter, the material and method in this thesis are briefly mentioned. In the fourth chapter, some basic definitions about Riemannian manifolds, vector bundles and distributions are given. In the fifth chapter, Riemann submersions, principal tensor fields, covariant derivatives of principal tensor fields and curvatures are discussed. In the sixth chapter, harmonic maps, biharmonic maps, 𝑓-harmonic maps, 𝑓-biharmonic maps and bi-f-harmonic maps are defined and their basic properties are given. In the seventh chapter, which contains the original results of the thesis, the necessary and sufficient conditions for a Riemann submersion defined from a 3-dimensional Riemann manifold to be f-biharmonic map and bi-f-harmonic map are investigated and the original geometric characterizations are obtained. The last section is devoted to conclusions and recommendations.