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Mathematics
Volume 13
Issue 21
10.3390/math13213411
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Yanlin Li
1,
Osman Keçilioğlu
2,
Kazım İlarslan
2 and
Qingyou Sun
1,*
1
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2
Department of Mathematics, Faculty of Engineering and Natural Sciences, Kırıkkale University, Kırıkkale 71450, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(21), 3411; https://doi.org/10.3390/math13213411 (registering DOI)
Submission received: 18 September 2025 / Revised: 13 October 2025 / Accepted: 20 October 2025 / Published: 26 October 2025
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
Versions Notes

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 Cartan null curves; Da Rios vortex filament equations; Combescure related curves

Share and Cite

MDPI and ACS Style

Li, Y.; Keçilioğlu, O.; İlarslan, K.; Sun, Q. Solutions of Da Rios Vortex Filament Equation of Cartan Null Curves with Combescure Transformation. Mathematics 2025, 13, 3411. https://doi.org/10.3390/math13213411

AMA Style

Li Y, Keçilioğlu O, İlarslan K, Sun Q. Solutions of Da Rios Vortex Filament Equation of Cartan Null Curves with Combescure Transformation. Mathematics. 2025; 13(21):3411. https://doi.org/10.3390/math13213411

Chicago/Turabian Style

Li, Yanlin, Osman Keçilioğlu, Kazım İlarslan, and Qingyou Sun. 2025. "Solutions of Da Rios Vortex Filament Equation of Cartan Null Curves with Combescure Transformation" Mathematics 13, no. 21: 3411. https://doi.org/10.3390/math13213411

APA Style

Li, Y., Keçilioğlu, O., İlarslan, K., & Sun, Q. (2025). Solutions of Da Rios Vortex Filament Equation of Cartan Null Curves with Combescure Transformation. Mathematics, 13(21), 3411. https://doi.org/10.3390/math13213411

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