Abstract
A local normal form is obtained for geodesics in the space Λ = {Γ} of analytic Jordan curves in the extended complex plane with symmetric space multiplication Γ1 · Γ2 defined by Schwarzian reflection of Γ2 in Γ1. Local geometric features of (Λ, ·) will be seen to reflect primarily the structure of the Witt algebra, while issues of global behavior of the exponential map will be viewed in the context of conformal mapping theory.