Geodesics transformations on Riemann and non-Riemann geometries

In this thesis Geodesics transformations on Riemann and non-Riemann geometries has been studied in three parts. The first part of this study includes the introduction. In the introduction, the starting point of Riemann geometry, manifold theory and Weyl geometry are given and general information about geodesic transformation is given. The second part includes basic concepts and definitions. In this section, the definitions of curved space, curved frame, curved coordinate, Euclidean space, Euclidean frame and Euclidean coordinate are given. Differentiable functions and curves on surfaces are studied. Then, by examining the connections on Riemannian space, basic definitions and theorems such as Riemannian curvature tensor, conformal curvature tensor, first and second type Bianchi identities for Riemannian curvature tensor, and Einstein space; definition are given. Similarly, curvature tensors of Weyl space and their corresponding identities are presented by making an analogy on the Weyl space. Conformal transformations related to Weyl space are mentioned. In the third chapter, definitions of geodesic, geodesic path, geodesic beam and geodesic space are given. Finally, geodesic equations and their solutions for an example are analyzed and compared under both Riemannian and Weyl spaces. In the last chapter of the thesis, the results obtained and suggestions for further studies are presented.