الفهرس 
Chapter 1: IntroductionOnly 14 pages are availabe for public view
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Abstract
Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century. It deals with a broad range of geometries whose metric properties vary from point to point, including the standard types of Non-Euclidean geometry. Lyra has proposed a modification of Riemannian geometry by introducing a gauge function into the structure less manifold that bears a close resemblance to Weyl’s geometry. Teleparallel gravity was an attempt by Albert Einstein to base a unified theory of electromagnetism and gravity on the mathematical structure of distant parallelism, also referred to as absolute or teleparallelism. In this thesis we study self –similarity of space-time based on different geometries. Mainly in Riemannian, Lyra geometries and teleparallel gravity we study cosmological models of Bianchi type I and Bianchi type V in mentioned geometries. The aim of this thesis is how to get the system of ten P.D.E of the homothetic motion in Riemannian geometry, Lyra geometry and Weitzenböck geometry comparing between them and solve each system taking the models Bianchi- type I and V. The thesis consists of four chapters, organized as follows: In Chapter1: we give the necessary definitions and concepts used through this work. In Chapter2: We calculate the homothetic vector field based on Riemannian geometry of the models Bianchi- type I and Bianchi- type V. In Chapter3: We calculate the homothetic vector field based on Lyra geometry of the models Bianchi -type I and Bianchi- type V.
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In Chapter4: We calculate the ten equations of HVF based on Weitzenböck geometry of the models Bianchi -type I and Bianchi- type V.