American Institute of Mathematical Sciences

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

Geometric equivalence on nonholonomic three-manifolds

Kurt Ehlers 1,

1. 

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

Received  September 2002 Revised  April 2003 Published  April 2003

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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