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In this paper we prove that automorphisms are the only isometries betweenrank two Almost-Riemannian Structures on the class of nonnilpotent, solvable,connected 3D Lie groups. As a consequence, a classification result for rank twoARSs on the groups in question is obtained.

Isometries of Almost-Riemannian structures on nonnilpotent, solvable 3D Lie groups