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Rolling Against a Sphere The Non-transitive Case

Abstract : We study the control system of a Riemannian manifold M of dimension n rolling on the sphere . The controllability of this system is described in terms of the holonomy of a vector bundle connection which, we prove, is isomorphic to the Riemannian holonomy group of the cone C(M) of M. Using Berger's list, we reduce the possible holonomies to a few families. In particular, we focus on the cases where the holonomy is the unitary and the symplectic group. In the first case, using the rolling formalism, we construct explicitly a Sasakian structure on M; and in the second case, we construct a 3-Sasakian structure on M.
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Submitted on : Friday, April 3, 2020 - 9:51:18 AM
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Yacine Chitour, Mauricio Godoy Molina, Petri Kokkonen, Irina Markina. Rolling Against a Sphere The Non-transitive Case. The Journal of Geometric Analysis, Springer, 2016, 26 (4), pp.2542-2562. ⟨10.1007/s12220-015-9638-y⟩. ⟨hal-02307514⟩

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