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Geometric equivalence on nonholonomic three-manifolds

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  • 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.
    Mathematics Subject Classification: Primary: 70G45,53C10,37J60; Secondary: 58A17.


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