Geometry of coupled dispersionless equations with Mannheim curves
In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is considered. A connection with the coupled disp...
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| Format: | Article |
| Language: | English |
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Sciendo
2023-09-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2023-0034 |
| _version_ | 1797653363609829376 |
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| author | Eren Kemal |
| author_facet | Eren Kemal |
| author_sort | Eren Kemal |
| collection | DOAJ |
| description | In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is considered. A connection with the coupled dispersionless equation and Mannheim curve pair is established. Also, the Lax pair of the obtained coupled dispersionless equation from the motions of any Mannheim curve pair is given. This gives us a significant condition based on the curvature and torsion of any Mannheim curve for its integrability since it is well-known that the Lax pair provides the integrability of di erential equations. |
| first_indexed | 2024-03-11T16:42:36Z |
| format | Article |
| id | doaj.art-b22b11f0a8aa49faa2ca542682a6a295 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-03-11T16:42:36Z |
| publishDate | 2023-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-b22b11f0a8aa49faa2ca542682a6a2952023-10-23T07:51:32ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352023-09-0131311112310.2478/auom-2023-0034Geometry of coupled dispersionless equations with Mannheim curvesEren Kemal01Sakarya University, Technology Developing Zones Manager CO., Sakarya, 54050, Turkey.In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is considered. A connection with the coupled dispersionless equation and Mannheim curve pair is established. Also, the Lax pair of the obtained coupled dispersionless equation from the motions of any Mannheim curve pair is given. This gives us a significant condition based on the curvature and torsion of any Mannheim curve for its integrability since it is well-known that the Lax pair provides the integrability of di erential equations.https://doi.org/10.2478/auom-2023-0034mannheim curvescoupled dispersionless equationslax pairsprimary 53a04secondary 35q70 |
| spellingShingle | Eren Kemal Geometry of coupled dispersionless equations with Mannheim curves Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica mannheim curves coupled dispersionless equations lax pairs primary 53a04 secondary 35q70 |
| title | Geometry of coupled dispersionless equations with Mannheim curves |
| title_full | Geometry of coupled dispersionless equations with Mannheim curves |
| title_fullStr | Geometry of coupled dispersionless equations with Mannheim curves |
| title_full_unstemmed | Geometry of coupled dispersionless equations with Mannheim curves |
| title_short | Geometry of coupled dispersionless equations with Mannheim curves |
| title_sort | geometry of coupled dispersionless equations with mannheim curves |
| topic | mannheim curves coupled dispersionless equations lax pairs primary 53a04 secondary 35q70 |
| url | https://doi.org/10.2478/auom-2023-0034 |
| work_keys_str_mv | AT erenkemal geometryofcoupleddispersionlessequationswithmannheimcurves |