Given that a connected Lie group with nilpotent radical acts transitively by isometries on a connected Riemannian manifold , the structure of the full connected isometry group of and the imbedding of in are described. In particular, if equals its derived subgroup and its Levi factors are of noncompact type, then is normal in . In the special case of a simply transitive action of on , a transitive normal subgroup of is constructed with and a sufficient condition is given for local isomorphism of and .
Étant donné un groupe de Lie connexe , dont le radical est nilpotent et qui opère transitivement par isométries sur un espace homogène riemannien , on décrit la structure du plus grand groupe connexe des isométries de et l’inclusion de dans . En conséquence, on obtient une condition suffisante pour que soit normal dans . Dans le cas spécial d’une action simplement transitive de sur , on construit un sous-groupe normal dans , transitif sur et ayant la même dimension que , et on donne une condition suffisante pour que soit localement isomorphe à .
@article{AIF_1981__31_2_193_0, author = {Gordon, C.}, title = {Transitive riemannian isometry groups with nilpotent radicals}, journal = {Annales de l'Institut Fourier}, pages = {193--204}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {31}, number = {2}, year = {1981}, doi = {10.5802/aif.835}, mrnumber = {82i:53040}, zbl = {0441.53034}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.835/} }
TY - JOUR AU - Gordon, C. TI - Transitive riemannian isometry groups with nilpotent radicals JO - Annales de l'Institut Fourier PY - 1981 SP - 193 EP - 204 VL - 31 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.835/ DO - 10.5802/aif.835 LA - en ID - AIF_1981__31_2_193_0 ER -
Gordon, C. Transitive riemannian isometry groups with nilpotent radicals. Annales de l'Institut Fourier, Volume 31 (1981) no. 2, pp. 193-204. doi : 10.5802/aif.835. http://www.numdam.org/articles/10.5802/aif.835/
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