Geodesics in the Heisenberg Group

Abstract

We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.

Keywords

• heisenberg group
• geodesics
• fourier series
• isoperimetric inequality