Symmetry of embedded genus 1 helicoids
J Bernstein, C Breiner - 2011 - projecteuclid.org
J Bernstein, C Breiner
2011•projecteuclid.orgIn this article, we use the Lopez-Ros deformation to show that any embedded genus 1
helicoid (or “genus-one helicoid”) must be symmetric with respect to rotation by 180° around
a normal line. This partially answers a conjecture of Bobenko. We also show that this
symmetry holds for an embedded genus k helicoid Σ, provided that the underlying conformal
structure of Σ is hyperelliptic.
helicoid (or “genus-one helicoid”) must be symmetric with respect to rotation by 180° around
a normal line. This partially answers a conjecture of Bobenko. We also show that this
symmetry holds for an embedded genus k helicoid Σ, provided that the underlying conformal
structure of Σ is hyperelliptic.
Abstract
In this article, we use the Lopez-Ros deformation to show that any embedded genus helicoid (or “genus-one helicoid”) must be symmetric with respect to rotation by around a normal line. This partially answers a conjecture of Bobenko. We also show that this symmetry holds for an embedded genus helicoid , provided that the underlying conformal structure of is hyperelliptic.
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