Bonnet pairs, isothermic surfaces and the retraction form

Abstract

We give a modern account of the classical theory of Bianchi \cite{Bia03} (see also \cite{KamPedPin98}) relating isothermic surfaces to Bonnet pairs. The main novelty is to identify the derivatives of the Bonnet pair with a component of the retraction form of the isothermic surface.

6 A4 pages. v2: add authors, correct typos