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.
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© 2013 Springer Basel
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Volchkov, V.V., Volchkov, V.V. (2013). Symmetric Spaces of the Non-compact Type. In: Offbeat Integral Geometry on Symmetric Spaces. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0572-8_3
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DOI: https://doi.org/10.1007/978-3-0348-0572-8_3
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0571-1
Online ISBN: 978-3-0348-0572-8
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