Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces
Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces τr,m minimally immersed in spheres to a three-parametric family Ta,b,c of tori and Klein bottles minimally immersed in spheres. It was remarked that this fa...
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| Дата: | 2016 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147428 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces / B. Causley // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ. |
Репозитарії
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irk-123456789-1474282019-02-15T01:24:12Z Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces Causley, B. Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces τr,m minimally immersed in spheres to a three-parametric family Ta,b,c of tori and Klein bottles minimally immersed in spheres. It was remarked that this family includes surfaces carrying all extremal metrics for the first non-trivial eigenvalue of the Laplace-Beltrami operator on the torus and on the Klein bottle: the Clifford torus, the equilateral torus and surprisingly the bipolar Lawson Klein bottle τ¯₃,₁. In the present paper we show in Theorem 1 that this three-parametric family Ta,b,c includes in fact all bipolar Lawson tau-surfaces τ¯r,m. In Theorem 3 we show that no metric on generalized Lawson surfaces is maximal except for τ¯₃,₁ and the equilateral torus. 2016 Article Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces / B. Causley // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58E11; 58J50; 49Q05; 35P15 DOI:10.3842/SIGMA.2016.009 http://dspace.nbuv.gov.ua/handle/123456789/147428 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Recently Penskoi [J. Geom. Anal. 25 (2015), 2645-2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces τr,m minimally immersed in spheres to a three-parametric family Ta,b,c of tori and Klein bottles minimally immersed in spheres. It was remarked that this family includes surfaces carrying all extremal metrics for the first non-trivial eigenvalue of the Laplace-Beltrami operator on the torus and on the Klein bottle: the Clifford torus, the equilateral torus and surprisingly the bipolar Lawson Klein bottle τ¯₃,₁. In the present paper we show in Theorem 1 that this three-parametric family Ta,b,c includes in fact all bipolar Lawson tau-surfaces τ¯r,m. In Theorem 3 we show that no metric on generalized Lawson surfaces is maximal except for τ¯₃,₁ and the equilateral torus. |
| format |
Article |
| author |
Causley, B. |
| spellingShingle |
Causley, B. Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Causley, B. |
| author_sort |
Causley, B. |
| title |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces |
| title_short |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces |
| title_full |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces |
| title_fullStr |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces |
| title_full_unstemmed |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces |
| title_sort |
bipolar lawson tau-surfaces and generalized lawson tau-surfaces |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147428 |
| citation_txt |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces / B. Causley // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 29 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT causleyb bipolarlawsontausurfacesandgeneralizedlawsontausurfaces |
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2025-07-11T02:03:41Z |
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2025-07-11T02:03:41Z |
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1837314260803256320 |