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dc.contributor.author |
Causley, B. |
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dc.date.accessioned |
2019-02-14T18:30:28Z |
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dc.date.available |
2019-02-14T18:30:28Z |
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dc.date.issued |
2016 |
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dc.identifier.citation |
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. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 58E11; 58J50; 49Q05; 35P15 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2016.009 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/147428 |
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dc.description.abstract |
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. |
uk_UA |
dc.description.sponsorship |
This result was obtained during studies of the author at the National Research University –
Higher School of Economics, Moscow and the author is very grateful for its hospitality. The
author also thanks A.V. Penskoi for the statement of this problem, many useful discussions and
invaluable help in preparing this manuscript. The research of the author was partially supported
by an NSERC Postgraduate Fellowship and by AG Laboratory NRU-HSE, Russian Federation
government grant, ag. 11.G34.31.0023. |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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