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Rolling against a sphere: The non transitive case | | Yacine Chitour
; Mauricio Godoy Molina
; Petri Kokkonen
; Irina Markina
; | | Date: |
23 Dec 2014 | | 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 $M$. | | Source: | arXiv, 1412.7218 | | Services: | Forum | Review | PDF | Favorites | |
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