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Geometriae Dedicata

, Volume 167, Issue 1, pp 233–238 | Cite as

A sufficient condition for congruency of orbits of Lie groups and some applications

  • Akira KuboEmail author
  • Hiroshi Tamaru
Original Paper

Abstract

We give a sufficient condition for isometric actions to have the congruency of orbits, that is, all orbits are isometrically congruent to each other. As applications, we give simple and unified proofs for some known congruence results, and also provide new examples of isometric actions on symmetric spaces of noncompact type which have the congruency of orbits.

Keywords

Congruency of orbits Isometric actions  Symmetric spaces of noncompact type Parabolic subgroups 

2010 Mathematics Subject Classification

Primary 57S20 Secondary 53C40 53C35 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan

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