TY - JOUR

T1 - Constrained Willmore and CMC tori in the 3-sphere

AU - Heller, Lynn

N1 - 13 pages

PY - 2015

Y1 - 2015

N2 - Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface \Sigma, such that f can be reconstructed in terms of algebraic data on \Sigma. Particularly interesting examples of constrained Willmore tori are the tori with constant mean curvature (CMC) in a 3-dimensional space form. It is shown in [14] and in [16] that the spectral curves of these tori are hyperelliptic. In this paper we show under mild conditions that a constrained Willmore torus f in the 3-sphere is a CMC torus in a 3-dimensional space form if its spectral curve has the structure of a CMC spectral curve.

AB - Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface \Sigma, such that f can be reconstructed in terms of algebraic data on \Sigma. Particularly interesting examples of constrained Willmore tori are the tori with constant mean curvature (CMC) in a 3-dimensional space form. It is shown in [14] and in [16] that the spectral curves of these tori are hyperelliptic. In this paper we show under mild conditions that a constrained Willmore torus f in the 3-sphere is a CMC torus in a 3-dimensional space form if its spectral curve has the structure of a CMC spectral curve.

KW - math.DG

KW - 53A05, 53A10, 53A30, 53C43

U2 - 10.1016/j.difgeo.2015.03.003

DO - 10.1016/j.difgeo.2015.03.003

M3 - Article

JO - Differ. Geom. Appl.,

JF - Differ. Geom. Appl.,

ER -