Given a Riemannian submersion between two Riemannian manifolds, we can lift the Riemannian structure from the target space to the source and in some cases we will obtain naturally a sub-Riemannian structure on the latter. For example, this is the case of sub-Riemannian principal bundles. In this talk I will present a work in progress in collaboration with E. Grong (Luxembourg) to find sub-Riemannian geodesics at this level of generality, which is motivated by the octonionic Hopf fibration.

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