Symmetry of Embedded Genus-One Helicoids

Details Symmetry of Embedded Genus-One Helicoids Symmetry of Embedded Genus-One Helicoids

2010-11-16

arxiv.org/abs/1011.3769v1

Mathematics

Differential Geometry

11 pages, 1 figure

Scientific paper

In this note, we use the Lopez-Ros deformation introduced in [9] to show that any embedded genus-one helicoid must be symmetric with respect to rotation by 180 degrees around a normal line. This partially answers a conjecture of Bobenko from [3]. We also show this symmetry holds for an embedded genus-k helicoid $\Sigma$, provided the underlying conformal structure of $\Sigma$ is hyperelliptic.

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