ON THE CHARACTERIZATIONS OF SPECIAL ADJOINT CURVES AND SURFACE FAMILY FOR THE MODIFIED ORTHOGONAL FRAME WITH TORSION
MATHEMATICA BOHEMICA, 2025 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2025
- Doi Numarası: 10.21136/mb.2025.0068-25
- Dergi Adı: MATHEMATICA BOHEMICA
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
In this context, the main interest of this paper is to construct a family of surfaces in E3 space which is the adjoint pair of a given curve. Then, using the modified orthogonal frame with torsion, we express the necessary conditions for the surface family that recognize the adjoint curve as a geodesic curve, an asymptotic curve and a line of curvature. Also, the singular points of the surface given by the parametric equation are expressed. It is concluded that the adjoint curve of the alpha curve whose torsion is not constant can not be geodesic on the surface under any circumstances. In addition, the case where the adjoint curve of the unit velocity alpha curve with nonconstant torsion with respect to the modified orthogonal frame with torsion is the Salkowski curve, is also exemplified. By the way, this work is illustrated by several examples.