Browsing by Author "Mohamed Alamin Abdalla Hamid"

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    Symmetric Spaces and Their Applications
    (Neelain University, 2007) Mohamed Alamin Abdalla Hamid
    Abstract Syrnrnet:n'c spaces is a special topic in Riemannian geometry . These spaces werefirst studied and classified by Elie Cartan . _ In this research we study in a logical ordering their snucture through manifolds , Lie groups , Lie algebras and basics of Riemannian geometry. _ The study covers locally and globally symmetric spaces , endowed with some examples for them such as Euclidean spaces , spheres hyperbolic spaces and some applications on locally syrrunetric spaces in the field of arithmetic and algebraic groups , including quadratic and modular fonns , lattices , the realization of discrete series representations of groups , Poincare and linear symmetric spaces . Their classification is also discussed by introducing compact and noncompact symmetric spaces besides the types ( l , ll , Ill , IV ) . This classification is carried through Lie algebras , root systems and their Dynkin diagrams . The aim of the research is to display in a simplified manner the connection between symmetric spaces and the differential geometric temis such as manifolds , Lie groups , Lie algebras and basics of Riemannian geometry with some of the applications of symmetric spaces.
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    Symmetric Spaces and Their Applications
    (Al Neelain University, 2007-02) Mohamed Alamin Abdalla Hamid
    Symmetric spaces is a special topic in Riemannian geometry . These spaces were first studied and classified by Elie Cartan . In this research we study in a logical ordering their stnicture through manifolds . Lie groups . Lie algebras and basics of Riemannian geometry. The study covers locally and globally symmetric spaces . endowed with some examples for them such as Euclidean spaces . spheres hyperbolic spaces and some applications on locally symmetric spaces in the field of arithmetic and algebraic groups , including quadratic and modular forms , lattices . the realization of discrete series representations of groups . Poincare and linear symmetric spaces . Their classification is also discussed by introducing compact and noncompact symmetric spaces besides the types ( l . ll . lll . l\‘ ) . This classification is carried tluough Lie algebras . root systems and their Dynkin diagrams t The aim ofthe research is to display in a simplified manner the connection between symmetric spaces and the differential geometric terms such as manifolds . Lie groups , Lie algebras and basics of Riemannian geometry with some of the applications of symmetric spaces.