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Annals of Global Analysis and Geometry

, Volume 37, Issue 2, pp 125–141 | Cite as

Parabolic symmetric spaces

  • Lenka ZalabováEmail author
Original Paper

Abstract

We study here systems of symmetries on |1|-graded parabolic geometries. We are interested in smooth systems of symmetries, and we discuss non-flat homogeneous |1|-graded geometries. We show the existence of an invariant admissible affine connection under quite weak condition on the system.

Keywords

Cartan geometries Parabolic geometries |1|-graded geometries Weyl structures Symmetric spaces 

Mathematics Subject Classification (2000)

53C15 53A40 53C05 53C35 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Eduard Čech Center for Algebra and Geometry, Faculty of ScienceMasaryk UniversityBrnoCzech Republic

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