[Sur deux théorèmes portant sur les automorphismes locaux des structures géométriques]
Cet article s’intéresse à des questions autour des orbites des automorphismes locaux de variétés munies de structures géométriques rigides. Nous formulons des conditions suffisantes assurant l’homogénéité locale d’un large spectre de structures géométriques rigides, les géométries de Cartan, étendant ainsi un résultat de Singer sur les variétés riemanniennes localement homogènes. Nous revisitons également un résultat très général de Gromov qui décrit l’agencement des orbites des automorphismes locaux des variétés munies de -structures rigides. Nous donnons un énoncé et une preuve élémentaire de ce résultat dans le cadre des géométries de Cartan.
This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give sufficient conditions for local homogeneity in a broad class of such structures, namely Cartan geometries, extending a classical result of Singer about locally homogeneous Riemannian manifolds. We also revisit a strong result of Gromov which describes the structure of the orbits of local automorphisms of manifolds endowed with -rigid structures, and give a statement and a simpler proof of this result in the setting of Cartan geometries.
Accepté le :
Publié le :
DOI : 10.5802/aif.3009
Keywords: Cartan geometries, local homogeneity, orbits of local automorphisms
Mot clés : Géométries de Cartan, homogénéité locale, orbites des automorphismes locaux
@article{AIF_2016__66_1_175_0,
author = {Pecastaing, Vincent},
title = {On two theorems about local automorphisms of geometric structures},
journal = {Annales de l'Institut Fourier},
pages = {175--208},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {1},
year = {2016},
doi = {10.5802/aif.3009},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3009/}
}
TY - JOUR AU - Pecastaing, Vincent TI - On two theorems about local automorphisms of geometric structures JO - Annales de l'Institut Fourier PY - 2016 SP - 175 EP - 208 VL - 66 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3009/ DO - 10.5802/aif.3009 LA - en ID - AIF_2016__66_1_175_0 ER -
%0 Journal Article %A Pecastaing, Vincent %T On two theorems about local automorphisms of geometric structures %J Annales de l'Institut Fourier %D 2016 %P 175-208 %V 66 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3009/ %R 10.5802/aif.3009 %G en %F AIF_2016__66_1_175_0
Pecastaing, Vincent. On two theorems about local automorphisms of geometric structures. Annales de l'Institut Fourier, Tome 66 (2016) no. 1, pp. 175-208. doi : 10.5802/aif.3009. http://www.numdam.org/articles/10.5802/aif.3009/
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