SOME SPECIAL CURVES IN DUAL 3-SPACE

Yıl 2019, Cilt: 2 Sayı: 1, 60 - 67, 30.01.2019

Beyhan Yılmaz

https://doi.org/10.33773/jum.506492

Öz

Rectifying, normal and osculating curves have been worked on many times in dierent spaces. The aim of this paper is to characterize these curves from another point of view in three dimensional Dual space.

Anahtar Kelimeler

Rectifying curve, osculating curve

Kaynakça

• A. Yücesan, N. Ayyıldız and A. C. Coken, On Rectifying Dual Space Curves, Revista Matematica Complutense, 20, 497-506, (2007).B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?,Amer. Math. Monthly, 110, 147{152 (2003).E. Study, Geometrie der Dynamen, Leibzig, (1903). G. Oztürk, A. Küçük and K. Arslan, Some Characteristic Properties of AW(k)-type Curves on Dual Unit Sphere, Extracta Mathematicae, 29, (1-2), 167-175, (2014).G. R. Veldkamp, On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics, Mech. Mach. Theory 11, no. 2, 141{156 (1976).J. Logan and Y. M. Oh, Characterization of Rectifying and Sphere Curves in R3; American Journal of Undergraduate Research. 14, 2 (2017). M. Do Carmo, Di_erential geometry of curves and surfaces, Prentice-Hall, Upper Saddle Riv. N.J., 1976. Ö. Köse, S. Nizamoğlu and M. Sezer, An explicit characterization of dual spherical curves, Do_ga Mat. 12, no. 3, 105{113 (1988). R. A. Abdel Baky, An Explicit Characterization of Dual Spherical Curve, Commun. Fac. Sci. Univ. Ank. Series A1, 51(2), 1-9, (2002).S. Ozkaldi, K. İlarslan and Y. Yaylı, On Mannheim Partner Curve in Dual Space, An. St. Univ. Ovidius Constanta, 17(2), 131-142, (2009). W. K. Cli_ord, Preliminary Sketch of bi-Quaternions, Proceedings of London Mathematical Society, 65, 361-395, (1873).