Polynomial conserved quantities for constrained Willmore surfaces
Differential Geometry
2019-04-01 v3
Abstract
We define a hierarchy of special classes of constrained Willmore surfaces by means of the existence of a polynomial conserved quantity of some type, filtered by an integer. Type 1 with parallel top term characterises parallel mean curvature surfaces and, in codimension 1, type 1 characterises constant mean curvature surfaces. We show that this hierarchy is preserved under both spectral deformation and Baecklund transformation, for special choices of parameters, defining, in particular, transformations of constant mean curvature surfaces into new ones, with preservation of the mean curvature, in the latter case.
Cite
@article{arxiv.1507.01253,
title = {Polynomial conserved quantities for constrained Willmore surfaces},
author = {Áurea Casinhas Quintino and Susana Duarte Santos},
journal= {arXiv preprint arXiv:1507.01253},
year = {2019}
}
Comments
v2: Abstract, Introduction and necessary background reformulated v3: minor corrections implemented