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Contact and conformal maps on Iwasawa N groups

Michael CowlingFilippo De MariAdam KorányiHans Martin Reimann — 2002

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The action of the conformal group O 1 , n + 1 on R n may be characterized in 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 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 parabolic subgroup. We solve...

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