Contact and conformal maps on Iwasawa N groups

Cowling, Michael, et al. "Contact and conformal maps on Iwasawa N groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.3-4 (2002): 219-232. <http://eudml.org/doc/252360>.

@article{Cowling2002,
abstract = {The action of the conformal group $O(1,n + 1)$ on $\mathbb\{R\}^\{n\} \cup \\{\infty\\}$ 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 $\mathbb\{R\}^\{n\}$ whose differential is a (variable) multiple of a (variable) isometry at each point of $U$ is the restriction to $U$ of a transformation $x \rightarrow g \cdot x$, 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 this problem for the cases where $G$ is $SL(3,\mathbb\{R\})$ or $Sp(2,\mathbb\{R\})$ and $P$ is a minimal parabolic subgroup.},
author = {Cowling, Michael, De Mari, Filippo, Korányi, Adam, Reimann, Hans Martin},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {semisimple Lie group; contact map; conformal map},
language = {eng},
month = {12},
number = {3-4},
pages = {219-232},
publisher = {Accademia Nazionale dei Lincei},
title = {Contact and conformal maps on Iwasawa N groups},
url = {http://eudml.org/doc/252360},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Cowling, Michael
AU - De Mari, Filippo
AU - Korányi, Adam
AU - Reimann, Hans Martin
TI - Contact and conformal maps on Iwasawa N groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/12//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 3-4
SP - 219
EP - 232
AB - The action of the conformal group $O(1,n + 1)$ on $\mathbb{R}^{n} \cup \{\infty\}$ 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 $\mathbb{R}^{n}$ whose differential is a (variable) multiple of a (variable) isometry at each point of $U$ is the restriction to $U$ of a transformation $x \rightarrow g \cdot x$, 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 this problem for the cases where $G$ is $SL(3,\mathbb{R})$ or $Sp(2,\mathbb{R})$ and $P$ is a minimal parabolic subgroup.
LA - eng
KW - semisimple Lie group; contact map; conformal map
UR - http://eudml.org/doc/252360
ER -