Hypersurface Constrained Elasticae in Lorentzian Space Forms
We study geodesics in hypersurfaces of a Lorentzian space form M1n+1(c), which are critical curves of the M1n+1(c)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic M13(c) a...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/458178 |
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| author | Óscar J. Garay Álvaro Pámpano Changhwa Woo |
| author_facet | Óscar J. Garay Álvaro Pámpano Changhwa Woo |
| author_sort | Óscar J. Garay |
| collection | DOAJ |
| description | We study geodesics in hypersurfaces of a Lorentzian space form M1n+1(c), which are critical curves of the M1n+1(c)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic M13(c) and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics. |
| format | Article |
| id | doaj-art-94ab883960804d02bda38c4112cdeb73 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-94ab883960804d02bda38c4112cdeb732025-02-03T00:59:00ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/458178458178Hypersurface Constrained Elasticae in Lorentzian Space FormsÓscar J. Garay0Álvaro Pámpano1Changhwa Woo2Department of Mathematics, Faculty of Science and Technology, Apartado 644, 48080 Bilbao, SpainDepartment of Mathematics, Faculty of Science and Technology, Apartado 644, 48080 Bilbao, SpainDepartment of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, Republic of KoreaWe study geodesics in hypersurfaces of a Lorentzian space form M1n+1(c), which are critical curves of the M1n+1(c)-bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic M13(c) and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3-space foliated by critical geodesics.http://dx.doi.org/10.1155/2015/458178 |
| spellingShingle | Óscar J. Garay Álvaro Pámpano Changhwa Woo Hypersurface Constrained Elasticae in Lorentzian Space Forms Advances in Mathematical Physics |
| title | Hypersurface Constrained Elasticae in Lorentzian Space Forms |
| title_full | Hypersurface Constrained Elasticae in Lorentzian Space Forms |
| title_fullStr | Hypersurface Constrained Elasticae in Lorentzian Space Forms |
| title_full_unstemmed | Hypersurface Constrained Elasticae in Lorentzian Space Forms |
| title_short | Hypersurface Constrained Elasticae in Lorentzian Space Forms |
| title_sort | hypersurface constrained elasticae in lorentzian space forms |
| url | http://dx.doi.org/10.1155/2015/458178 |
| work_keys_str_mv | AT oscarjgaray hypersurfaceconstrainedelasticaeinlorentzianspaceforms AT alvaropampano hypersurfaceconstrainedelasticaeinlorentzianspaceforms AT changhwawoo hypersurfaceconstrainedelasticaeinlorentzianspaceforms |