GENELLEŞTİRİLMİŞ KUATERNİYONLARIN SERRET-FRENET VE BISHOP ÇATILARI

Başlangıç: 2020
Yayıncı: Kütahya Dumlupınar Üniversitesi

Serret-Frenet ve Paralel taşıma çatıları, genelleştirilmiş kuaterniyonlar yardımıyla yine [4]te verilen metot ile oluşturulmuştur.

Anahtar Kelimeler:

Generalized quaternion, Serret-Frenet frame, Bishop frame

Serret-Frenet and Parallel-Transport frame are produced with the help of the generalized quaternions again by the method in [4].

Keywords:

[1] Inoguchi, J., ”Timelike surfaces of constant mean curvature in Minkowski 3- space”, Tokyo J. Math. 21(1) 141-152, 1998.
[2] Niven, I., ”The roots of a quaternion”, Amer. Math. Monthly 449(6) 386-388, 1942.
[3] Özdemir, M., Ergin A. A., ”Rotations with timelike quaternions in Minkowski 3-space”, J. Geom. Phys. 56 322-336, 2006
[4] Hanson, A. J., ”Quaternion Frenet Frames: Making Optimal Tubes and Ribbons from Curves”, Tech. Rep. 407, Indiana Unv. Computer Science Dep., 1994.
[5] Eisenhart, L. P., ”A Treatise on the Differential Geometry of Curves and Surfaces”, Dover, New York, 1960, Originally published in 1909.
[6] Flanders, H., Differential Forms with Applications to Physical Sciences”, Academic Press, New York, 1963.
[7] Gray, A., ”Modern Differential Geometry of Curves and Surfaces”, CRC Press, Inc., Boca Raton, FL, 1993.
[8] Struik, D. J., ”Lectures on Classical Differential Geometry”, Addison-Wesley, 1961
[9] Öztürk, U., Hacısalihoğlu, H. H., Yaylı, Y., Koç Öztürk, E. B. ,”Dual Quaternion Frames”, Commun. Fac. Sci. Univ. Ank. Series A1 59(2) 41–50, 2010
[10] Bishop, R. L., ”There is more than one way to frame a curve”, Amer. Math. Monthly 82(3) , 246-251, March 1975.