Geodesic
Some Basic Results Concerning G-invariant Riemannian Metrics
Journal of Lie theory, Tome 18 (2008) no. 1, pp. 243-251.

Voir la notice de l'article provenant de la source Heldermann Verlag

we study complete $G$-invariant Riemannian metrics. Let $G$ be a Lie group and let $M$ be a proper smooth $G$-manifold. Let $\alpha$ be a smooth $G$-invariant Riemannian metric of $M$, and let $\tilde{K}$ be any $G$-compact subset of $M$. We show that $M$ admits a complete smooth $G$-invariant Riemannian metric $\beta$ such that $\beta\vert \tilde{K}=\alpha\vert \tilde{K}$. We also prove the existence of complete real analytic $G$-invariant Riemannian metrics for proper real analytic $G$-manifolds. Moreover, we show that for any given smooth (real analytic) $G$-invariant Riemannian metric there exists a complete smooth (real analytic) $G$-invariant Riemannian metric conformal to the original Riemannian metric. To prove the real analytic results we need the assumption that $G$ can be embeddded as a closed subgroup of a Lie group which has only finitely many connected components.
Classification : 57S20
Mots-clés : Lie groups, Riemannian metric, real analytic 
@article{JLT_2008_18_1_JLT_2008_18_1_a14,
     author = {M. Kankaanrinta },
     title = {Some {Basic} {Results} {Concerning} {G-invariant} {Riemannian} {Metrics}},
     journal = {Journal of Lie theory},
     pages = {243--251},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a14/}
}
TY  - JOUR
AU  - M. Kankaanrinta 
TI  - Some Basic Results Concerning G-invariant Riemannian Metrics
JO  - Journal of Lie theory
PY  - 2008
SP  - 243
EP  - 251
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a14/
ID  - JLT_2008_18_1_JLT_2008_18_1_a14
ER  - 
%0 Journal Article
%A M. Kankaanrinta 
%T Some Basic Results Concerning G-invariant Riemannian Metrics
%J Journal of Lie theory
%D 2008
%P 243-251
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a14/
%F JLT_2008_18_1_JLT_2008_18_1_a14
M. Kankaanrinta . Some Basic Results Concerning G-invariant Riemannian Metrics. Journal of Lie theory, Tome 18 (2008) no. 1, pp. 243-251. http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a14/