Willmore immersions and loop groups

Abstract

We propose a characterisation of Willmore immersions inspired from the works of R. Bryant on Willmore surfaces and J. Dorfmeister, F. Pedit, H.-Y. Wu on harmonic maps between a surface and a compact homogeneous manifold using moving frames and loop groups. We use that formulation in order to construct a Weierstrass type representation of all conformal Willmore immersions in terms of closed one-forms. © 1998 Applied Probability Trust.