Bonnet pairs, isothermic surfaces and the retraction form

Published 16 Jun 2025 in math.DG | (2506.13312v2)

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.

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