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Geometric equivalence on nonholonomic three-manifolds
We apply Cartan’s method of equivalence to the case of nonholonomic
geometry on three-dimensional contact manifolds. Our main result is to derive the
differential invariants for these structures and give geometric interpretations. We
show that the symmetry group of such a structure has dimension at most four. Our
motivation is to study the geometry associated with classical mechanical systems
with nonholonomic constraints.