Sub-Finsler Geometry
Jeanne Nielsen-Clelland
Department of Mathematics
 University of Colorado, Boulder


Motivated by examples from control theory, we consider the notion of  sub-Finsler geometry and show how it is a natural  generalization of sub-Riemannian geometry.  We use Cartan's method of equivalence to compute invariants for sub-Finsler structures on 3-manifolds, and we find an invariant which vanishes if and only if  the sub-Finsler structure is sub-Riemannian.  We also derive geodesic equations and classify the homogeneous examples in the 3-dimensional  case.  If time permits, we will also present some preliminary results along these lines in the 4-dimensional case.