Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces
We define a Lie bracket on a certain set of local vector fields along a null curve in a 4-dimensional semi-Riemannian space form. This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space. In particular, a geometric recursi...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/5725234 |
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| author | José del Amor Ángel Giménez Pascual Lucas |
| author_facet | José del Amor Ángel Giménez Pascual Lucas |
| author_sort | José del Amor |
| collection | DOAJ |
| description | We define a Lie bracket on a certain set of local vector fields along a null curve in a 4-dimensional semi-Riemannian space form. This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space. In particular, a geometric recursion operator generating infinitely many local symmetries for the null localized induction equation is provided. |
| format | Article |
| id | doaj-art-867577feacca4aca895f55eb51b49f85 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-867577feacca4aca895f55eb51b49f852025-02-03T06:05:45ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/57252345725234Null Curve Evolution in Four-Dimensional Pseudo-Euclidean SpacesJosé del Amor0Ángel Giménez1Pascual Lucas2Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, SpainCentro de Investigación Operativa, Universidad Miguel Hernández de Elche, Avenida Universidad s/n, Elche, 03202 Alicante, SpainDepartamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, SpainWe define a Lie bracket on a certain set of local vector fields along a null curve in a 4-dimensional semi-Riemannian space form. This Lie bracket will be employed to study integrability properties of evolution equations for null curves in a pseudo-Euclidean space. In particular, a geometric recursion operator generating infinitely many local symmetries for the null localized induction equation is provided.http://dx.doi.org/10.1155/2016/5725234 |
| spellingShingle | José del Amor Ángel Giménez Pascual Lucas Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces Advances in Mathematical Physics |
| title | Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces |
| title_full | Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces |
| title_fullStr | Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces |
| title_full_unstemmed | Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces |
| title_short | Null Curve Evolution in Four-Dimensional Pseudo-Euclidean Spaces |
| title_sort | null curve evolution in four dimensional pseudo euclidean spaces |
| url | http://dx.doi.org/10.1155/2016/5725234 |
| work_keys_str_mv | AT josedelamor nullcurveevolutioninfourdimensionalpseudoeuclideanspaces AT angelgimenez nullcurveevolutioninfourdimensionalpseudoeuclideanspaces AT pascuallucas nullcurveevolutioninfourdimensionalpseudoeuclideanspaces |