Geometries from a Symmetry Point of View

Abstract

This study basically aims to discuss the topic of Geometries from a Symmetry Point of View. In this study we discovered that the unifying feature of several physical phenomena can be described by some geometric structures defined on space. The geometric structure should be invariant under a transformation group. We considered Hamiltonian mechanics as a set up for analytical mechanical phenomena. We also considered in some sort of generality Cartan structure equations that described the general variations. Finally, the study leads to classification problems of different geometric structure and their applications.