2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106177In this paper we study Moebius applicable surfaces, i.e., conformally immersed surfaces in Moebius 3-space which admit deformations preserving the Moebius metric. We show new characterizations of Willmore surfaces, Bonnet surfaces and Harmonic inverse mean curvature surfaces in terms of Moebius or similarity invariants.17pagesDifferential Geometry53A10; 37K25Deformations of surfaces preserving conformal or similarity invariantstext