Sub-Riemannian geometry on the group of motions of the plane

Abstract: We will discuss the unique, up to local isometries, contact sub-Riemannian struc ture on the group SE(2) of proper motions of the plane (aka group of rototransla tions). The following questions will be addressed:

1.   geodesics,
2.   their local and global optimality,
3.   cut time, cut locus, and spheres,
4.   infinite geodesics,
5.   bicycle transform and relation of geodesics with Euler elasticae,
6.   group of isometries and homogeneous geodesics,
7.   applications to imaging and robotics.

Joint work with Andrei Ardentov.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( slides | video )

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Geometry of differential equations seminar

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