Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces
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| Creator |
Causley, B.
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| 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.
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| Date |
2019-02-14T18:30:28Z
2019-02-14T18:30:28Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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