Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers
This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-07-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0069 |
| _version_ | 1818738561608843264 |
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| author | Castro Ildefonso Castro-Infantes Ildefonso Castro-Infantes Jesús |
| author_facet | Castro Ildefonso Castro-Infantes Ildefonso Castro-Infantes Jesús |
| author_sort | Castro Ildefonso |
| collection | DOAJ |
| description | This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in 𝕃2 and provide the Lorentzian versions of catenaries and grim-reaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically. |
| first_indexed | 2024-12-18T01:10:54Z |
| format | Article |
| id | doaj.art-f0d8390d5afd49289b0ff91a3fcb146f |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-18T01:10:54Z |
| publishDate | 2018-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-f0d8390d5afd49289b0ff91a3fcb146f2022-12-21T21:26:06ZengDe GruyterOpen Mathematics2391-54552018-07-0116174776610.1515/math-2018-0069math-2018-0069Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapersCastro Ildefonso0Castro-Infantes Ildefonso1Castro-Infantes Jesús2Departamento de Matemáticas, Universidad de Jaén, 23071Jaén, Spain and Instituto de Matemáticas (IEMath-GR)Departamento de Geometría y Topología, Universidad de Granada, 18071Granada, Spain and Instituto de Matemáticas (IEMath-GR)Departamento de Geometría y Topología, Universidad de Granada, 18071Granada, SpainThis article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane 𝕃2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in 𝕃2 and provide the Lorentzian versions of catenaries and grim-reaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically.https://doi.org/10.1515/math-2018-0069lorentzian curvescurvatureelastic curvescatenariesgrim-reaper curves53a3514h5053b3074h05 |
| spellingShingle | Castro Ildefonso Castro-Infantes Ildefonso Castro-Infantes Jesús Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers Open Mathematics lorentzian curves curvature elastic curves catenaries grim-reaper curves 53a35 14h50 53b30 74h05 |
| title | Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers |
| title_full | Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers |
| title_fullStr | Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers |
| title_full_unstemmed | Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers |
| title_short | Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers |
| title_sort | curves in the lorentz minkowski plane elasticae catenaries and grim reapers |
| topic | lorentzian curves curvature elastic curves catenaries grim-reaper curves 53a35 14h50 53b30 74h05 |
| url | https://doi.org/10.1515/math-2018-0069 |
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