The action of the conformal group \group{O}(1,n+1) on \pip^n\cup\{\infty\} 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 \pip^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\mapstog\cdotx, for some g in {\rmO}(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 this problem for the cases where G is {\rmSL}(3,\pip) or {\rmSp}(2,\pip) and P is a minimal parabolic subgroup
Contact and conformal maps on Iwasawa N groups
DE MARI CASARETO DAL VERME, FILIPPO;
2002-01-01
Abstract
The action of the conformal group \group{O}(1,n+1) on \pip^n\cup\{\infty\} 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 \pip^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\mapstog\cdotx, for some g in {\rmO}(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 this problem for the cases where G is {\rmSL}(3,\pip) or {\rmSp}(2,\pip) and P is a minimal parabolic subgroup
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