Symmetry of embedded genus 1 helicoids
In 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...
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| Veröffentlicht in: | Duke mathematical journal 2011-07, Vol.159 (1), p.83-97 |
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| container_title | Duke mathematical journal |
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| creator | Bernstein, Jacob Breiner, Christine |
| description | In 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. |
| doi_str_mv | 10.1215/00127094-1384791 |
| format | Article |
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| identifier | ISSN: 0012-7094 |
| ispartof | Duke mathematical journal, 2011-07, Vol.159 (1), p.83-97 |
| issn | 0012-7094 1547-7398 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1310416363 |
| source | Project Euclid Complete |
| subjects | 14H40 37K10 bi-Hamiltonian structures Completely integrable systems etc. hierarchies (KdV integrability tests Jacobians Prym varieties [See also 32G20] Toda |
| title | Symmetry of embedded genus 1 helicoids |
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