Seminar talk, 14 April 2021

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Speaker: Yuri Sachkov

Title: 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:

  • geodesics,
  • their local and global optimality,
  • cut time, cut locus, and spheres,
  • infinite geodesics,
  • bicycle transform and relation of geodesics with Euler elasticae,
  • group of isometries and homogeneous geodesics,
  • applications to imaging and robotics.

Joint work with Andrei Ardentov.

Language: English