Contact and conformal maps in parabolic geometry. I

Abstract

When n >= 3, the action of the conformal group O( 1, n+1) on R(n)boolean OR{infinity} may be characterized in simple differential geometric terms, even locally: a theorem of Liouville states that a C-4 map between domains U and V in R-n whose differential is a ( variable) multiple of a ( variable) isometry at each point of U is the restriction to U of a transformation x -> g center dot 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.