2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79992A novel class of integrable surfaces is recorded. This class of O surfaces is shown to include and generalize classical surfaces such as isothermic, constant mean curvature, minimal, `linear' Weingarten, Guichard and Petot surfaces and surfaces of constant Gaussian curvature. It is demonstrated that the construction of a Backlund transformation for O surfaces leads in a natural manner to an associated parameter-dependent linear representation. The classical pseudosphere and breather pseudospherical surfaces are generated.19 pages, 2 figuresExactly Solvable and Integrable SystemsDifferential Geometrytext