Bianchi-B\"{a}cklund transforms and dressing actions, revisited

TL;DR

This paper revisits Bianchi-Bäcklund transformations for surfaces with positive constant Gauss curvature, framing them as dressing actions on harmonic maps, providing a new perspective on their geometric and algebraic structure.

Contribution

It offers a novel characterization of Bianchi-Bäcklund transformations as dressing actions on harmonic maps, linking classical surface theory with modern integrable systems.

Findings

Bianchi-Bäcklund transformations are characterized via dressing actions.

The approach connects classical surface transformations with harmonic map theory.

Provides a unified framework for understanding transformations of constant curvature surfaces.

Abstract

We characterize Bianchi-B\"{a}cklund transformations of surfaces of positive constant Gauss curvature in terms of dressing actions of the simplest type on the space of harmonic maps.