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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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | 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 |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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