Abstract
This work is dedicated to the study of the Möbius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric connections; Bäcklund transformations, by applying a dressing action; and, in 4space, Darboux transformations, based on the solution of a Riccati equation. We establish a permutability between spectral deformation and Bäcklund transformation and prove that nontrivial Darboux transformation of constrained Willmore surfaces in 4space can be obtained as a particular case of Bäcklund transformation.
All these transformations corresponding to the zero multiplier preserve the class of Willmore surfaces. We verify that, for special choices of parameters, both spectral deformation and Bäcklund transformation preserve the class of constrained Willmore surfaces admitting a conserved quantity, and, in particular, the class of CMC surfaces in 3dimensional spaceform. The spectral deformation preserves the isothermic condition.
Date of Award  20 May 2009 

Original language  English 
Awarding Institution 

Supervisor  Fran Burstall (Supervisor) 