A note on hyperbolic flows in sub-Riemannian structures with transverse symmetries (Q663437)

The present note studies the hyperbolicity of the flows associated with a natural mechanical system in a sub-Riemannian structure with multidimensional symmetries. In this case, the sub-Riemannian structure is reduced to a Riemannian one with a vector-valued magnetic field. Sufficient conditions for the hyperbolicity of the reduced Hamiltonian are expressed by means of the Riemannian curvature tensor and the magnetic field. As a consequence, new classes of Anosov flows are given.