Geometry of the non-degenerate Hasimoto-like surfaces for the classification of pseudo-null curve evolution using Darboux triad
International Journal of Geometric Methods in Modern Physics, cilt.22, sa.11, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 22 Sayı: 11
- Basım Tarihi: 2025
- Doi Numarası: 10.1142/s0219887825501208
- Dergi Adı: International Journal of Geometric Methods in Modern Physics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: Hasimoto surface, vortex filament equation, NLS- equation, Darboux triad, pseudo-null curve
- Kırklareli Üniversitesi Adresli: Evet
Özet
In my work, non-degenerate Hasimoto surfaces were studied for the second and third types of pseudo-null curve evolution associated with Darboux triad in 3D Minkowski space. The non-degenerate Hasimoto-like surfaces were obtained based on whether these surfaces are associated with NLS− equation, using Darboux triad of the pseudo-null curve. Within the same geometric framework, the differentials of the second and third Hasimoto-like transformations were formalized. Various geometric properties of these types of surfaces, such as the Gaussian curvature, the mean curvature, the harmonicity, and the conditions for being umbilic surfaces, were investigated. Additionally, a detailed explanation of the parameter curves for these surfaces was provided, using Darboux triad of the pseudo-null curve.