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|Title:||Symmetric Spaces and Their Applications|
|Authors:||Mohamed Alamin Abdalla Hamid|
|Abstract:||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.|
|Description:||Thesis Submiﬁed in Fulfillmem‘ For Phd. Degree In Mafhemafics|
|Appears in Collections:||PHD theses : Statistics|
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