Transformations of harmonic bundles and Willmore surfaces
@article{Quintino2011TransformationsOH,
title={Transformations of harmonic bundles and Willmore surfaces},
author={{\'A}urea Casinhas Quintino},
journal={arXiv: Differential Geometry},
year={2011}
}Willmore surfaces are the extremals of the Willmore functional (possibly under a constraint on the conformal structure). With the characterization of Willmore surfaces by the (possibly perturbed) harmonicity of the mean curvature sphere congruence [Blaschke, Ejiri, Rigoli, Burstall-Calderbank], a zero-curvature formulation follows [Burstall-Calderbank]. Deformations on the level of harmonic maps prove to give rise to deformations on the level of surfaces, with the definition of a spectral…
References
SHOWING 1-7 OF 7 REFERENCES
Constrained Willmore Surfaces
- Mathematics
- 2009
This work is dedicated to the study of the Moebius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric…
A duality theorem for Willmore surfaces
- Mathematics
- 1984
so the two functional differ by a constant. The functional i^(X) has the advantage that its integrand is nonnegative and vanishes exactly at the umbilic points of the immersion X. Obviously iT(X) = 0…
Constrained Willmore surfaces
- Mathematics
- 2004
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $${\mathcal{W}} = \int H^2$$ under compactly supported infinitesimal…
Conformal submanifold geometry I-III
- Mathematics
- 2010
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…
Special isothermic surfaces of type d
- MathematicsJ. Lond. Math. Soc.
- 2012
The special isothermic surfaces, discovered by Darboux in connection with deformations of quadrics, admit a simple explanation via the gauge-theoretic approach to is othermic surfaces and extend the theory to arbitrary codimension.