Conformal semi-invariant riemannian maps to sasakian manifolds

This thesis consists of four chapters. In the first chapter, detailed information is provided about Riemann maps and the studies conducted on these maps. The second chapter introduces the fundamental concepts that serve as the theoretical foundation of the thesis. In this context, Riemannian manifolds, complex manifolds, Riemann maps, semi-invariant Riemann maps, and Sasakian manifolds are presented. The third chapter contains the original contributions of the study. In this section, the concept of conformal semi-invariant Riemann maps, previously introduced by Şahin and Akyol [31] for almost Hermitian manifolds, is extended to Sasakian manifolds, which are contact metric manifolds. In this regard, conformal semi-invariant Riemann maps defined from Riemannian manifolds to Sasakian manifolds are examined. A non-trivial example of such maps is given, and the geometry of the distributions D_1,D_2 〖,D ̅〗_1, D ̅_2 is investigated. Furthermore, necessary and sufficient conditions for these maps to be totally geodesic are obtained, and their harmonicity is analyzed. In the fourth and final chapter, potential directions for future research related to conformal semi-invariant Riemann maps are discussed. Keywords: Semi-invariant Riemann maps, Conformal semi-invariant Riemann maps, Sasakian manifolds