Geometric equivalence on nonholonomic three-manifolds

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2003, 2003(Special): 246-255. doi: 10.3934/proc.2003.2003.246

Geometric equivalence on nonholonomic three-manifolds

1.	Truckee Meadows Community College, 7000 Dandini Blvd, Reno, NV 89512, United States

Received September 2002 Revised April 2003 Published April 2003

Abstract
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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.

Keywords: G-structures., Nonholonomic mechanics, equivalence method.

Mathematics Subject Classification: Primary: 70G45,53C10,37J60; Secondary: 58A1.

Citation: Kurt Ehlers. Geometric equivalence on nonholonomic three-manifolds. Conference Publications, 2003, 2003 (Special) : 246-255. doi: 10.3934/proc.2003.2003.246

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