Concircular transformations on Weyl space with special metric connection

Weyl spaces were introduced by Hermann Weyl in 1918 to formulate the unified field theory in physics. Although Weyl's work was not accepted at first, Weyl manifolds have been of interest to both physicists and mathematicians. This thesis consists of three parts. In the literature review, Riemannian manifolds, their geometric structures, their curvatures, and curvature related properties; afterwards, Weyl manifolds, and their geometric properties are given. In addition to these, Weyl spaces with semi-symmetric recurrent metric connection, and the curvatures of these spaces, their related properties and quantities are mentioned. It has been brought to the literature by proving the geometrical structure of semi-symmetric recurrent metric connection under the concircular transformation on Weyl manifolds, their symmetry properties, and the Bianchi identity under this tranformation. In the first part, the curvature tensors in Riemannian space, their symmetry properties, I. & II. Bianchi identities, and theorems are given. And then, Weyl space is represented with a similar analogy. In the second part, the concepts related to Weyl spaces are examined. Firstly, the definition of Weyl space is given, then the curvature, covariant curvature, Ricci curvature tensor, and scalar curvature of Weyl space are expressed in terms of Riemannian tensor, and the metric tensor. The symmetry properties of these tensors are observed. In the third and the last part, the concircular curvature tensor of Weyl space with semi-symmetric recurrent metric connection is proved under the circle-preserving (concircular) transformation. Symmetry properties of this curvature tensor, and I. Bianchi identity have been found.