Symmetric Spaces of the Non-compact Type

Valery V. Volchkov and Vitaly V. Volchkov
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Valery V. Volchkov: Donetsk National University, Department of Mathematics
Vitaly V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 3 in Offbeat Integral Geometry on Symmetric Spaces, 2013, pp 85-110 from Springer

Abstract: Abstract From a global viewpoint, a symmetric space is a Riemannian manifold which possesses a symmetry about each point, that is, an involutive isometry leaving the point fixed. This generalizes the notion of reflection in a point in ordinary Euclidean geometry. The theory of symmetric spaces implies that such spaces have a transitive group of isometries and can be represented as coset spaces G/K, where G is a connected Lie group with an involutive automorphism G whose fixed point set is (essentially) K.

Keywords: Symmetric Space; Transitive Group; Iwasawa Decomposition; Bibliographical Note; Involutive Automorphism (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-0348-0572-8_3

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