Isothermic submanifolds of symmetric $R$-spaces

Abstract

We extend the classical theory of isothermic surfaces in conformal 3-space, due to Bour, Christoffel, Darboux, Bianchi and others, to the more general context of submanifolds of symmetric $R$-spaces with essentially no loss of integrable structure.

arXiv comment35 pages, 3 figures. v2: typos and other infelicities corrected.

References in corpus (3)

• Isothermic surfaces in $\E^3$ as soliton surfaces
• Ricci-corrected derivatives and invariant differential operators
• Isothermic surfaces in sphere geometries as Moutard nets

Cited by in corpus (2)

• Generalised Bianchi permutability for isothermic surfaces
• Infinitesimal Darboux transformation and semi-discrete mKdV equation