Mazlum, Sümeyye Gür; Aksan, Birkan

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.

Aksan, Birkan; Mazlum, Sumeyye Gur

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space R31, Lorentzian sphere S21 and hyperbolic sphere H2 0 of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in R3 1 and draw the graphs of these indicatrix curves on the spheres.

Mazlum, Sümeyye Gür; Aksan, Birkan

Bu çalışmada 3-boyutlu Lorentz uzayında timelike asli normalli spacelike Salkowski eğrisinin pol gösterge eğrisinin Frenet çatısı, eğrilikleri, Frenet türev formülleri, Darboux vektörü, yay uzunluğu, e ve (Lorentzian küre) ye göre geodezik eğrilikleri hesaplanmıştır ve bu pol gösterge eğrisi Lorentzian küre üzerinde gösterilmiştir.