On Darboux Frames of Indicatrices of Spacelike Salkowski Curve with Spacelike Binormal in E13

Authors : Birkan Aksan, Sümeyye Gür Mazlum

Pages : 401-413

Doi:10.34248/bsengineering.1337888

View : 113 | Download : 107

Publication Date : 2023-10-15

Article Type : Research Paper

Abstract :The aim of this study is to examine Darboux frames and some other geometric properties (geodesic curvatures, geodesic torsions, normal curvatures, Darboux derivative formulas, Darboux vectors, angles, etc.) of the spherical indicatrices on Lorentzian unit sphere S_1^2 and hyperbolic unit sphere H_0^2 of the spacelike Salkowski curve with spacelike binormal in Lorentzian 3-space E_1^3. In this context, new and interesting results have been obtained for this curve. Thus, relationships between the newly obtained curvatures and torsions and the curvature and torsion of the original curve are given. Moreover, the matrix relationship between the Darboux and Frenet frames of these indicatrices is shown. Finally, the Darboux vectors belong to the Darboux frames and the Darboux vectors belong to the Frenet frames of these curves are compared.
Keywords : Lorentzian space, Salkowski curve, Darboux frame, Spherical indicatrices, Curvatures