When n3, the action of the conformal group O(1,n+1) on Rn∪{∞} may be characterized in simple differential geometric terms, even locally: a theorem of Liouville states that a C4 map between domains U and V in Rn whose differential is a (variable) multiple of a (variable) isometry at each point of U is the restriction to U of a transfor- mation x→g·x, for some g in O(1,n+1). In this paper, we consider the problem of char- acterizing the action of a more general semisimple Lie group G on the space G/P, where P is a minimal parabolic subgroup.
Contact and conformal mappings in parabolic geometry. I
DE MARI CASARETO DAL VERME F.;
2005-01-01
Abstract
When n3, the action of the conformal group O(1,n+1) on Rn∪{∞} may be characterized in simple differential geometric terms, even locally: a theorem of Liouville states that a C4 map between domains U and V in Rn whose differential is a (variable) multiple of a (variable) isometry at each point of U is the restriction to U of a transfor- mation x→g·x, for some g in O(1,n+1). In this paper, we consider the problem of char- acterizing the action of a more general semisimple Lie group G on the space G/P, where P is a minimal parabolic subgroup.
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