Solutions of Da Rios Vortex Filament Equation of Cartan Null Curves with Combescure Transformation

Yanlin Li, Osman Keçilioğlu, Kazım İlarslan and Qingyou Sun ()
Additional contact information
Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Osman Keçilioğlu: Department of Mathematics, Faculty of Engineering and Natural Sciences, Kırıkkale University, Kırıkkale 71450, Turkey
Kazım İlarslan: Department of Mathematics, Faculty of Engineering and Natural Sciences, Kırıkkale University, Kırıkkale 71450, Turkey
Qingyou Sun: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Mathematics, 2025, vol. 13, issue 21, 1-15

Abstract: In this study, Cartan null curves connected via the Combescure transformation are investigated within the framework of Minkowski 3-space, and the necessary conditions for establishing such connections are derived. The relationships between the Frenet vectors and curvatures of these curve pairs are also analyzed. Furthermore, when a ruled surface generated by a Cartan null curve provides a solution to the Da Rios equation, the conditions under which the ruled surface generated was by the corresponding Cartan null curve, related through the Combescure transformation, also satisfies the equation. All obtained results are supported with illustrative examples.

Keywords: Cartan null curves; Da Rios vortex filament equations; Combescure related curves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3411/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3411/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3411-:d:1780034

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().