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Title: Symmetric Spaces and Their Applications
Authors: Mohamed Alamin Abdalla Hamid
Keywords: Symmetric Spaces
Issue Date: 2007
Publisher: Neelain University
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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