Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One

@inproceedings{Berndt2005CohomogeneityOA,
  title={Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One},
  author={J{\"u}rgen Berndt and Hiroshi Tamaru},
  year={2005}
}
We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CH, n ≥ 3. For the quaternionic hyperbolic spaces HH, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classification problem was essentially solved by Élie Cartan. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 25 references

Cohomogeneity one actions on hyperbolic spaces

  • J. Berndt, M. Brück
  • J. Reine Angew. Math
  • 2001
Highly Influential
8 Excerpts

Familles de surfaces isoparamétriques dans les espaces à courbure constante

  • E. Cartan
  • Ann. Mat. pura appl. IV. s
  • 1938
Highly Influential
10 Excerpts

Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit

  • J. Berndt, H. Tamaru
  • Tôhoku Math. J
  • 2004
1 Excerpt

Homogeneous codimension one foliations on noncompact symmetric spaces

  • J. Berndt, H. Tamaru
  • J. Differential Geom
  • 2003
2 Excerpts

Minimal homogeneous submanifolds of symmetric spaces. In: Lie groups and symmetric spaces: in memory of F.I

  • D. V. Alekseevsky, A. J. Di Scala
  • Karpelevich (Ed. S.G. Gindikin), Amer. Math. Soc…
  • 2003
2 Excerpts

Calibrated geometries

  • H. B. Lawson
  • Geometry of nonpositively curved manifolds
  • 1996

Geometry of nonpositively curved manifolds

  • P. B. Eberlein
  • 1996
1 Excerpt

Generalized Heisenberg groups and Damek-Ricci harmonic spaces. Lecture Notes in Mathematics 1598

  • J. Berndt, F. Tricerri, L. Vanhecke
  • 1995
1 Excerpt

Similar Papers

Loading similar papers…