Asian Journal of Mathematics
Volume 11 (2007)
Geometry of Sub-Finsler Engel Manifolds
Pages: 699 – 726
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.
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.