Transitive riemannian isometry groups with nilpotent radicals
Annales de l'Institut Fourier, Volume 31 (1981) no. 2, p. 193-204

Given that a connected Lie group G with nilpotent radical acts transitively by isometries on a connected Riemannian manifold M, the structure of the full connected isometry group A of M and the imbedding of G in A are described. In particular, if G equals its derived subgroup and its Levi factors are of noncompact type, then G is normal in A. In the special case of a simply transitive action of G on M, a transitive normal subgroup G of A is constructed with dimG =dimG and a sufficient condition is given for local isomorphism of G and G.

Étant donné un groupe de Lie connexe G, dont le radical est nilpotent et qui opère transitivement par isométries sur un espace homogène riemannien M, on décrit la structure du plus grand groupe connexe A des isométries de M et l’inclusion de G dans A. En conséquence, on obtient une condition suffisante pour que G soit normal dans A. Dans le cas spécial d’une action simplement transitive de G sur M, on construit un sous-groupe G normal dans A, transitif sur M et ayant la même dimension que G, et on donne une condition suffisante pour que G soit localement isomorphe à G.

@article{AIF_1981__31_2_193_0,
     author = {Gordon, C.},
     title = {Transitive riemannian isometry groups with nilpotent radicals},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {31},
     number = {2},
     year = {1981},
     pages = {193-204},
     doi = {10.5802/aif.835},
     zbl = {0441.53034},
     mrnumber = {82i:53040},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1981__31_2_193_0}
}
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/item/AIF_1981__31_2_193_0/

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