On Dini Helicoids in the Minkowski Space
The Dini helicoid is a surface obtained by a screw motion of the tractrix. In this paper, we consider various analogs of the Dini helicoid in the three-dimensional Minkowski space. As profiles, we take nontrivial pseudo-Euclidean analogs of the tractrix different from pseudo-Euclidean circles. We pr...
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 276; no. 4; pp. 517 - 524 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.11.2023
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-023-06772-9 |
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| Abstract | The Dini helicoid is a surface obtained by a screw motion of the tractrix. In this paper, we consider various analogs of the Dini helicoid in the three-dimensional Minkowski space. As profiles, we take nontrivial pseudo-Euclidean analogs of the tractrix different from pseudo-Euclidean circles. We prove that on analogs of the Dini helicoid in a the pseudo-Euclidean space, one of the following metrics is induced: the metric of the Lobachevsky plane, the metric of the de Sitter plane, or a degenerate metric. |
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| AbstractList | The Dini helicoid is a surface obtained by a screw motion of the tractrix. In this paper, we consider various analogs of the Dini helicoid in the three-dimensional Minkowski space. As profiles, we take nontrivial pseudo-Euclidean analogs of the tractrix different from pseudo-Euclidean circles. We prove that on analogs of the Dini helicoid in a the pseudo-Euclidean space, one of the following metrics is induced: the metric of the Lobachevsky plane, the metric of the de Sitter plane, or a degenerate metric. The Dini helicoid is a surface obtained by a screw motion of the tractrix. In this paper, we consider various analogs of the Dini helicoid in the three-dimensional Minkowski space. As profiles, we take nontrivial pseudo-Euclidean analogs of the tractrix different from pseudo-Euclidean circles. We prove that on analogs of the Dini helicoid in a the pseudo-Euclidean space, one of the following metrics is induced: the metric of the Lobachevsky plane, the metric of the de Sitter plane, or a degenerate metric. Keywords and phrases: Lobachevsky plane, de Sitter plane, Dini helicoid. AMS Subject Classification: 53A35, 53B30 |
| Audience | Academic |
| Author | Kostin, A. V. |
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| Copyright | Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. COPYRIGHT 2023 Springer |
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| References | Albujer, Caballero (CR1) 2017; 445 CR10 Bour (CR3) 1862; 39 Ikawa (CR6) 2001; 24 CR4 Ji, Kim (CR7) 2013; 220 Kostin (CR9) 2019; 21 Barros, Caballero, Ortega (CR2) 2009; 290 CR8 Lopez (CR11) 2014; 7 Lopez, Kaya (CR12) 2017; 71 Güler, Vanli (CR5) 2006; 46 T Ikawa (6772_CR6) 2001; 24 6772_CR10 F Ji (6772_CR7) 2013; 220 R Lopez (6772_CR12) 2017; 71 M Barros (6772_CR2) 2009; 290 E Bour (6772_CR3) 1862; 39 6772_CR8 AV Kostin (6772_CR9) 2019; 21 E Güler (6772_CR5) 2006; 46 AL Albujer (6772_CR1) 2017; 445 6772_CR4 R Lopez (6772_CR11) 2014; 7 |
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| Title | On Dini Helicoids in the Minkowski Space |
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