Abstract:
We will discuss the unique, up to local isometries, contact sub-Riemannian structure on the group SE(2) of proper motions of the plane (aka group of rototranslations).
The following questions will be addressed:
geodesics,
their local and global optimality,
cut time, cut locus, and spheres,
infinite geodesics,
bicycle transform and relation of geodesics with Euler elasticae,
