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The aim of this thesis is to show some mathematical concepts and methods of differential geometry and Lie groups. Subsequently, we try to use this tools in physics. Selection of these two mathematical topics is not random, because these topics are close related essentials of theoretical physics. The thesis is split into two chapters. Each chapter fulfils one of this aim. In the first chapter we introduce the notion of group, which is further enriched with other notions, like group action or group product. This detailed and smooth process leads us to introduction of homogeneous space which is one of the most important notion of Klein geometry. The end of this chapter is devoted to brief introduction to this attitude to geometry. The second chapter consists formulation of physical tasks in the language of differential geometry and afterwards its solution. As the final topic in this thesis we introduce Jacobi connection, as more natural option of connection which is implemented to physical system. Powered by TCPDF (www.tcpdf.org) |
