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In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point. This can be made more precise, in either the language of Riemannian geometry or of Lie theory. The Riemannian definition is more geometric, and plays a deep role in the theory of holonomy. The Lie-theoretic definition is more algebraic. From the point of view of Lie theory, a symmetric space is the quotient G/H of Lie group G by a Lie subgroup H, where the Lie algebra of H is also required to be the

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  • Symmetric space
  • Symmetrischer Raum
  • Espace symétrique
  • Симметрическое пространство
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  • In der Mathematik sind symmetrische Räume eine Klasse von Riemannschen Mannigfaltigkeiten mit einem besonders hohen Grad an Symmetrien. Sie sind eine wichtige Klasse von Beispielen in Geometrie und Topologie und finden Anwendung unter anderem in Darstellungstheorie, harmonischer Analysis, Zahlentheorie, Modulformen und Physik.
  • Симметрическое пространство — риманово многообразие, группа изометрий которого содержит центральные симметрии с центром в любой точке.
  • In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point. This can be made more precise, in either the language of Riemannian geometry or of Lie theory. The Riemannian definition is more geometric, and plays a deep role in the theory of holonomy. The Lie-theoretic definition is more algebraic. From the point of view of Lie theory, a symmetric space is the quotient G/H of Lie group G by a Lie subgroup H, where the Lie algebra of H is also required to be the
  • En mathématiques, et plus spécifiquement en géométrie différentielle, un espace riemannien symétrique est une variété riemannienne qui, en chaque point, admet une isométrie involutive dont ce point est un point fixe isolé. Plus généralement, un espace symétrique est une variété différentielle munie, en chaque point, d'une involution, le tout vérifiant certaines conditions. Lorsqu'il n'y pas de risque de confusion, les espaces riemanniens symétriques sont appelés espaces symétriques. Les espaces symétriques connexes sont des espaces homogènes de groupes de Lie.
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