Timelike Bonnet surfaces in the Lorentzian 3-space
UDC 519.11 We generalize the criteria proposed by Z. Soyu\c{c}ok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classific...
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8383 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513065311666176 |
|---|---|
| author | Kanbay, Filiz Yüksekdağ, Burcu Kanbay, Filiz Yüksekdağ, Burcu |
| author_facet | Kanbay, Filiz Yüksekdağ, Burcu Kanbay, Filiz Yüksekdağ, Burcu |
| author_sort | Kanbay, Filiz |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-08T09:36:22Z |
| description | UDC 519.11
We generalize the criteria proposed by Z. Soyu\c{c}ok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classification of helicoids proposed by Beneki, et al. We present nonisothermic timelike helicoids as examples illustrating our results. Thus, they satisfy the conditions as timelike Bonnet surfaces. In addition, we present the isothermic timelike minimal helicoids. |
| doi_str_mv | 10.3842/umzh.v77i3.8383 |
| first_indexed | 2026-03-24T03:38:45Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8383 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:45Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-83832025-11-08T09:36:22Z Timelike Bonnet surfaces in the Lorentzian 3-space Timelike Bonnet surfaces in the Lorentzian 3-space Kanbay, Filiz Yüksekdağ, Burcu Kanbay, Filiz Yüksekdağ, Burcu Bonnet surface, timelike surface, timelike helicoid, associate surface, A-net geometry UDC 519.11 We generalize the criteria proposed by Z. Soyu\c{c}ok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classification of helicoids proposed by Beneki, et al. We present nonisothermic timelike helicoids as examples illustrating our results. Thus, they satisfy the conditions as timelike Bonnet surfaces. In addition, we present the isothermic timelike minimal helicoids. УДК 519.11 Часоподібні поверхні Боннета в лоренцевому 3-просторі Критерії, запропоновані З. Соючок у 3-вимірному евклідовому просторі, узагальнено на 3-простір Лоренца для часоподібних поверхонь. За допомогою цього критерію досліджено неізотермічні часові поверхні Боннета та їхні асоційовані поверхні. Також розглянуто класифікацію гелікоїдів, запропоновану Бенекі та ін. Наведено неізотермічні часоподібні гелікоїди, що ілюструють отримані результати, та показано, що вони задовольняють умови як часові поверхні Боннета. Крім того, наведено ізотермічні часові мінімальні гелікоїди. Institute of Mathematics, NAS of Ukraine 2025-11-07 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8383 10.3842/umzh.v77i3.8383 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 3 (2025); 232 Український математичний журнал; Том 77 № 3 (2025); 232 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8383/10420 Copyright (c) 2025 Filiz Kanbay, Burcu Yüksekdağ |
| spellingShingle | Kanbay, Filiz Yüksekdağ, Burcu Kanbay, Filiz Yüksekdağ, Burcu Timelike Bonnet surfaces in the Lorentzian 3-space |
| title | Timelike Bonnet surfaces in the Lorentzian 3-space |
| title_alt | Timelike Bonnet surfaces in the Lorentzian 3-space |
| title_full | Timelike Bonnet surfaces in the Lorentzian 3-space |
| title_fullStr | Timelike Bonnet surfaces in the Lorentzian 3-space |
| title_full_unstemmed | Timelike Bonnet surfaces in the Lorentzian 3-space |
| title_short | Timelike Bonnet surfaces in the Lorentzian 3-space |
| title_sort | timelike bonnet surfaces in the lorentzian 3-space |
| topic_facet | Bonnet surface timelike surface timelike helicoid associate surface A-net geometry |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8383 |
| work_keys_str_mv | AT kanbayfiliz timelikebonnetsurfacesinthelorentzian3space AT yuksekdagburcu timelikebonnetsurfacesinthelorentzian3space AT kanbayfiliz timelikebonnetsurfacesinthelorentzian3space AT yuksekdagburcu timelikebonnetsurfacesinthelorentzian3space |