Mannheim Partner Curves According to Darboux Frame in the Euclidean 3-space E^3

Year 2020, Volume: 8 Issue: 2, 54 - 59, 15.10.2020

Abdullah Yıldırım , Feryat Kaya

https://doi.org/10.36753/mathenot.599866

Cited By: 3

Abstract

In this study, we consider Mannheim partner curves according to Darboux Frame. Characterization of Mannheim partner curves lying on the surface are examined, and some curves are obtained. The characteristics of these curves are given by the geodesic curvatures, normal curvatures and geodesic torsions of these curves.

..............................

....................................................

..................................

.................................

...................................

.............................

........................................

Keywords

Curves , Surface , Geodesics , Curvatures

References

• Coşkun, Ö.: 3-Boyutlu Öklid ve Minkowski Uzaylarında Mannheim Eğri Çiftleri. Ms. thesis. Uşak University (2010).
• Kaymaz, F., Kahraman, Aksoyak, F.: Some Special Curves and Mannheim Curves in Three Dimensional Euclidean Space. Mathematical Sciences and Applications E-Notes. 5(2), 34-39 (2017).
• Kazaz, M., Hüseyin, Uğurlu, H., Önder, M., Kahraman, T.: Manheim Partner D curves in the Euclidean 3-space E3. New Trends in Mathematical Sciences. 3(2), 24-35 (2015).
• Kazaz, M., Hüseyin, Uğurlu, H., Önder, M., Oral, S.: Bertrand Partner D-Curves in the Euclidean 3-space E3. Afyon Kocatepe Universty Journal of Science and Engineering. 16, 76-83 (2016).
• Liu, H., Wang, F.: Manheim Partner Curves in 3-Space. In: Proceeding of the Eleventh International Workshop on Differential Geometry, Daegu, SOUTH KOREA. 11, 25-31 (2007).
• Mannheim, A.: De l'emploi de la Courbe Représentative de la Surface des Normales Principales d'une Courbe Gauche Pour la Démonstration de Propriétés Relatives à Cette Courbure. Comptes Rendus des Séances de l'Académie des Sciences. 86, 1254–1256 (1878).
• Zeynep, Azak, A.: Üç Boyutlu Lorentz Uzayında Timelike Mannheim Eğri Çifti Üzerine. Sakarya University Journal of Science and Art. 11(2), 35-45 (2009).