%0 Journal Article
%T Conformal submanifold geometry I-III
%A Francis E. Burstall
%A David M. J. Calderbank
%J Mathematics
%D 2010
%I arXiv
%X In Part I, we develop the notions of a Moebius structure and a conformal Cartan geometry, establish an equivalence between them; we use them in Part II to study submanifolds of conformal manifolds in arbitrary dimension and codimension. We obtain Gauss-Codazzi-Ricci equations and a conformal Bonnet theorem characterizing immersed submanifolds of the conformal n-sphere. These methods are applied in Part III to study constrained Willmore surfaces, isothermic surfaces, Guichard surfaces and conformally-flat submanifolds with flat normal bundle, and their spectral deformations, in arbitrary codimension. The high point of these applications is a unified theory of Moebius-flat submanifolds, which include Guichard surfaces and conformally flat hypersurfaces.
%U http://arxiv.org/abs/1006.5700v1