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.