Conformal riemannian maps on complex geometry

Being prepared as a doctoral thesis, this study consists of five chapters. In the first chapter, historical development of the thesis subject is explained, and the problems that takes part in the thesis are introduced. In the second chapter, basic definitions and terms which will be used in the next sections, are discussed. In the third chapter, conformal Riemannian maps between Riemannian manifolds, and holomorphic conformal Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, conformal invariant Riemannian maps and conformal anti-invariant Riemannian maps are studied. Examples about these maps are given. A relation between a conformal invariant Riemannian map and a holomorphic conformal Riemannian map is analysed. The geometry of conformal anti-invariant Riemannian maps is analysed by means of pluriharmonic map notion, and some conditions are given to make it horizontally homothetic map. In the fourth chapter, conformal semi-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds are studied. Examples about these maps are given and the geometry of the distributions is analysed. Conditions are given for conformal semi-invariant Riemannian maps to be horizontally homothetic and geodesic. In the fifth chapter, conformal slant Riemannian maps from almost Hermitian ma-nifolds to Riemannian manifolds are studied. Examples about these maps are given. Conditions for distributions to be integrable are presented, the geometry that conformal slant Riemannian maps with pluriharmonic property is being researched and the conditions for conformal slant Riemannian maps to be geodesic are given.