References of "Godoy Molina, Mauricio"
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See detailRiemannian and Sub-Riemannian geodesic flow
Godoy Molina, Mauricio; Grong, Erlend UL

in Journal of Geometric Analysis (2016)

We show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This result ... [more ▼]

We show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This result allows us describe the sub-Riemannian geodesic flow on totally geodesic Riemannian foliations in terms of the Riemannian geodesic flow. Also, given a submersion $\pi:M \to B$, we describe when the projections of a Riemannian and a sub-Riemannian geodesic flow in $M$ coincide. [less ▲]

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See detailGeometric conditions for the existence of a rolling without twisting or slipping
Godoy Molina, Mauricio; Grong, Erlend UL

in Communications on Pure and Applied Analysis (2014), 13(1), 435-452

We give a complete answer to the question of when two curves in two different Riemannian manifolds can be seen as trajectories of rolling one manifold on the other without twisting or slipping. We show ... [more ▼]

We give a complete answer to the question of when two curves in two different Riemannian manifolds can be seen as trajectories of rolling one manifold on the other without twisting or slipping. We show that, up to technical hypotheses, a rolling along these curves exists if and only if the geodesic curvatures of each curve coincide. By using the anti-developments of the curves, which we claim can be seen as a generalization of the geodesic curvatures, we are able to extend the result to arbitrary absolutely continuous curves. For a manifold of constant sectional curvature rolling on itself, two such curves can only differ by an isometry. In the case of surfaces, we give conditions for when loops in the manifolds lift to loops in the configuration space of the rolling. [less ▲]

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