Willmore-Like Tori in Killing Submersions
The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized el...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/4652516 |
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| _version_ | 1832560820766113792 |
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| author | Manuel Barros Óscar J. Garay Álvaro Pámpano |
| author_facet | Manuel Barros Óscar J. Garay Álvaro Pámpano |
| author_sort | Manuel Barros |
| collection | DOAJ |
| description | The first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature. |
| format | Article |
| id | doaj-art-9c59ba28d5a54266b6dce6f805e93aee |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9c59ba28d5a54266b6dce6f805e93aee2025-02-03T01:26:41ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/46525164652516Willmore-Like Tori in Killing SubmersionsManuel Barros0Óscar J. Garay1Álvaro Pámpano2Departamento de Geometría y Topología, Universidad de Granada, Granada, SpainDepartment of Mathematics, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Bilbao, SpainDepartment of Mathematics, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Bilbao, SpainThe first variation formula and Euler-Lagrange equations for Willmore-like surfaces in Riemannian 3-spaces with potential are computed and, then, applied to the study of invariant Willmore-like tori with invariant potential in the total space of a Killing submersion. A connection with generalized elastica in the base surface of the Killing submersion is found, which is exploited to analyze Willmore tori in Killing submersions and to construct foliations of Killing submersions made up of Willmore tori with constant mean curvature.http://dx.doi.org/10.1155/2018/4652516 |
| spellingShingle | Manuel Barros Óscar J. Garay Álvaro Pámpano Willmore-Like Tori in Killing Submersions Advances in Mathematical Physics |
| title | Willmore-Like Tori in Killing Submersions |
| title_full | Willmore-Like Tori in Killing Submersions |
| title_fullStr | Willmore-Like Tori in Killing Submersions |
| title_full_unstemmed | Willmore-Like Tori in Killing Submersions |
| title_short | Willmore-Like Tori in Killing Submersions |
| title_sort | willmore like tori in killing submersions |
| url | http://dx.doi.org/10.1155/2018/4652516 |
| work_keys_str_mv | AT manuelbarros willmoreliketoriinkillingsubmersions AT oscarjgaray willmoreliketoriinkillingsubmersions AT alvaropampano willmoreliketoriinkillingsubmersions |