Deformations of Surfaces Preserving Conformal or Similarity Invariants.

We study Möbius applicable surfaces, i.e., conformally immersed surfaces in Möbius 3-space which admit deformations preserving the Möbius metric. We show new characterizations of Willmore surfaces, Bonnet surfaces and harmonic inverse mean curvature surfaces in terms of Möbius or similarity invariants. [ABSTRACT FROM AUTHOR]