<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Geometry of coupled dispersionless equations with Mannheim curves

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"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...

Geometry of coupled dispersionless equations with Mannheim curves

Published Online: Oct 21, 2023

Page range: 111 - 123

Received: Sep 19, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0034

Keywords
Mannheim curves, coupled dispersionless equations, Lax pairs

© 2023 Kemal Eren, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Geometry of coupled dispersionless equations with Mannheim curves

Published Online: Oct 21, 2023

Page range: 111 - 123

Received: Sep 19, 2022

Accepted: Dec 22, 2022

DOI: https://doi.org/10.2478/auom-2023-0034

KeywordsMannheim curves, coupled dispersionless equations, Lax pairs

© 2023 Kemal Eren, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Mannheim curves, coupled dispersionless equations, Lax pairs