Symmetries of the rolling model

Yacine Chitour 1 M.-G. Molina Petri Kokkonen
1 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : In the present paper, we study the infinitesimal symmetries of the model of two Riemannian manifolds (M, g) and ({\hat{M}},\hat{g}) rolling without twisting or slipping. We show that, under certain genericity hypotheses, the natural bundle projection from the state space Q of the rolling model onto M is a principal bundle if and only if {\hat{M}} has constant sectional curvature. Additionally, we prove that when M and {\hat{M}} have different constant sectional curvatures and dimension n\ge 3, the rolling distribution is never flat, contrary to the two dimensional situation of rolling two spheres of radii in the proportion 1{:}3, which is a well-known system satisfying É. Cartan’s flatness condition.
Type de document :
Article dans une revue
Mathematische Zeitschrift, Springer, 2015, 281 (4), pp.783-805. 〈10.1007/s00209-015-1508-6 〉
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Soumis le : mardi 9 février 2016 - 08:35:02
Dernière modification le : jeudi 27 septembre 2018 - 14:30:03

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Yacine Chitour, M.-G. Molina, Petri Kokkonen. Symmetries of the rolling model. Mathematische Zeitschrift, Springer, 2015, 281 (4), pp.783-805. 〈10.1007/s00209-015-1508-6 〉. 〈hal-01271285〉

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