On Riemannian maps in complex geometry

This study, which was prepared as a master's thesis, consists of five chapters. In the first chapter, the historical development of the subject and the problems discussed in this thesis are introduced. In the second part, basic definitions, theorems and concepts that will be useful in other parts are discussed. In the third chapter, invariant and anti-invariant Riemannian maps in complex geometry are studied. Under this title, invariant Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are defined and an example of the existence of this map is given. Then, anti-invariant Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are defined and an example of the existence of this maps is given. Finally, the parallel of the distributions and their being completely geodesic were investigated for these maps. In the fourth chapter, semi-invariant Riemannian maps defined Riemannian manifolds from almost Hermitian manifolds in complex geometry are studied. Under this title, semi-invariant Riemann maps defined Riemannian manifolds from almost Hermitian manifolds are introduced and an example of the existence of this map is given. Then, the integrability and parallelism of the distributions for these maps are examined. Finally, fully umbilical points and semi-invariant Riemannian maps were examined and a general result was obtained. In the fifth chapter, which is the last chapter, slant-Riemann maps defined Riemannian manifolds from almost Hermitian manifolds in complex geometry are studied. Under this title, firstly, slant-Riemannian maps, which are defined Riemannian manifolds from almost Hermitian manifolds, are introduced and an example of the existence of this map is given. Then, the conditions of being slant-Riemannian maps, being harmonic, paralell and being completely geodesic were examined and a general decomposition theorem was given.