Geometry of Sub-Finsler Engel Manifolds

We analyze the geometry of sub-Finsler Engel manifolds, computing a complete set of local invariants for a large class of these manifolds. We derive geodesic equations for regular geodesics and show that in the symmetric case, the rigid curves are local minimizers. We end by illustrating our results with an example.

Keywords

Sub-Finsler geometry, Engel manifolds, optimal control theory, exterior differential systems, Cartan's method of equivalence

2010 Mathematics Subject Classification

Primary 49J15, 53B40, 53C17. Secondary 53C10, 58A15.

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Published 1 January 2007