**Sub-Finsler Geometry**

Jeanne Nielsen-Clelland

Department of Mathematics

University of Colorado, Boulder
**Abstract**

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.