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arXiv · 1412.7218

Rolling against a sphere: The non transitive case

Yacine Chitour·Mauricio Godoy Molina·Petri Kokkonen·Irina Markina
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Abstract

We study the control system of a Riemannian manifold $M$ of dimension $n$ rolling on the sphere $S^n$. 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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Yacine Chitour, Mauricio Godoy Molina, Petri Kokkonen, Irina Markina. 2014-12-23. Rolling against a sphere: The non transitive case. https://arxiv.org/abs/1412.7218

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