Geodesic
Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III
Journal of Lie theory, Tome 16 (2006) no. 3, pp. 579-6.

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

Any sufficiently often differentiable curve in the orbit space V/G of a real finite dimensional orthogonal representation G to O(V) of a finite group G admits a differentiable lift into the representation space V with locally bounded derivative. As a consequence any sufficiently often differentiable curve in the orbit space V/G can be lifted twice differentiably which is in general best possible. These results can be generalized to arbitrary polar representations. Finite reflection groups and finite rotation groups in dimensions two and three are discussed in detail.
Classification : 22E45, 20F55
Mots-clés : Invariants, representations 
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     author = {A. Kriegl and M. Losik and P. W. Michor and A. Rainer },
     title = {Lifting {Smooth} {Curves} over {Invariants} for {Representations} of {Compact} {Lie} {Groups,} {III}},
     journal = {Journal of Lie theory},
     pages = {579--6},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_3_JLT_2006_16_3_a9/}
}
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A. Kriegl; M. Losik; P. W. Michor; A. Rainer . Lifting Smooth Curves over Invariants for Representations of Compact Lie Groups, III. Journal of Lie theory, Tome 16 (2006) no. 3, pp. 579-6. http://geodesic.mathdoc.fr/item/JLT_2006_16_3_JLT_2006_16_3_a9/