Geometriae Dedicata

, Volume 111, Issue 1, pp 65–86

Contact and Conformal Maps in

Parabolic Geometry. I

Authors

    • School of MathematicsUniversity of New South Wales
  • Filippo De Mari
    • DIPEMUniversità di Genova
  • Adam Korányi
    • Department of Mathematics and Computer ScienceLehman College
  • Hans Martin Reimann
    • Mathematisches InstitutUniversität Bern
Article

DOI: 10.1007/s10711-004-4231-8

Cite this article as:
Cowling, M., Mari, F.D., Korányi, A. et al. Geom Dedicata (2005) 111: 65. doi:10.1007/s10711-004-4231-8

Abstract

When \(n \geqslant 3,\) the action of the conformal group O(1, n+1) on \({\mathbb R}^n \cup\{\infty\}\) may be characterized in simple differential geometric terms, even locally: a theorem of Liouville states that a C4 map between domains \({\cal U}\) and \({\cal V}\) in \({\mathbb R}^n\) whose differential is a (variable) multiple of a (variable) isometry at each point of \({\cal U}\) is the restriction to \({\cal U}\) of a transformation xg·x, for some g in O(1,n+1). In this paper, we consider the problem of characterizing the action of a more general semisimple Lie group G on the space G/P, where P is a minimal parabolic subgroup.

Mathematics Subject Classifications (2000)

53C3053A3057S20

Keywords

semisimple Lie groupcontact mapconformal map

Copyright information

© Springer 2005