DE Seminar: Philip Arathoon (Babson College)

Title: Integrable sub-Riemannian geodesic flows
 
Abstract: Suppose you want to move your car to an adjacent parking space. Instead of sliding the car you must first reverse, then turn a bit, and then move forward. This is an example of a sub-Riemannian geometry where the length of a path is only defined for admissible curves. Another example is given by rolling a ball across a table without slipping. We discuss this example and its generalization to sub-Riemannian geodesics on the special orthogonal group, and ask to what extent can these geometries be realized as the limits of ordinary Riemannian metrics.