SPACELIKE CURVES OF CONSTANT BREADTH ACCORDING TO BISHOP FRAME IN MINKOWSKI 3-SPACE

Year 2015, Volume: 3 Issue: 1, 86 - 93, 15.05.2015

Hüseyin Kocayiğit , Muhammed Çetin

https://doi.org/10.36753/mathenot.421222

Cited By: 2

Abstract

Keywords

Bishop frame, Curve of constant breadth, Differential characterizations of curve, Minkowski space, Spacelike Curve

References

• [1] Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
• [2] Barbier, E., Note Sur le Probleme de I’aiguille et le jeu du Joint Couvert, Journal de Math´ematiques Pures et Appliqu´ees, 2 (1860), no. 5, 273-286.
• [3] Fujiwara, M., On space Curves of Constant Breadth, Tohoku Mathematical Journal, 5 (1914), 180-184.
• [4] Blaschke, W., Leibziger Berichte, 67 (1917), 290.
• [5] Ball, N.H., On Ovals, American Mathematical Monthly, 37 (1930), no. 7, 348-353.
• [6] Mellish, A.P., Notes on Differential Geometry, Annals of Mathematics, 32 (1931), no. 1, 181-190.
• [7] Hammer, P.C., Constant Breadth Curves in the Plane, Procedings of the American Mathematical Society, 6 (1955), no. 2, 333-334.
• [8] Smakal, S., Curves of Constant Breadth, Czechoslovak Mathematical Journal, 23 (1973), no. 1, 86-94.
• [9] Köse, O., Düzlemde Ovaller ve Sabit Genişlikli Eğrilerin Bazı Özellikleri, Doğa Bilim Dergisi, Seri B, 8 (1984), no. 2, 119-126.
• [10] Köse, O., On Space Curves of Constant Breadth, ¨ Do˘ga Tr. J. Math, 10 (1986), no. 1, 11-14. [11] Ma˘gden, A., and Köse, O., On the Curves of Constant Breadth in ¨ E4 Space, Tr. J. of Mathematics, 21 (1997), 277-284.
• [12] Akdoğan, Z., and Mağden, A., Some Characterization of Curves of Constant Breadth in En Space, Turk J Math, 25 (2001), 433-444.
• [13] Reuleaux, F., The Kinematics of Machinery, Translated by A. B. W. Kennedy, Dover Pub. New York, 1963.
• [14] Sezer, M., Differential Equations Characterizing Space Curves of Constant Breadth and a Criterion for These Curves, Turkish J. of Math, 13 (1989), no. 2, 70-78.
• [15] Onder, M., Kocayi˘git, H. and Candan, E., Differential Equations Characterizing Timelike ¨ and Spacelike Curves of Constant Breadth in Minkowski 3-Space E31, J. Korean Math. Soc. 48 (2011), no. 4, 849-866.
• [16] Kocayiğit, H. and Önder, M., Space Curves of Constant Breadth in Minkowski 3-Space, ¨ Annali di Matematica, 192 (2013), no. 5, 805-814.
• [17] O’Neill, B., Semi Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
• [18] Hanson, A.J. and Ma, H., Parallel Transport Approach to Curve Framing, Indiana University, Technical Report TR425, January 11, 1995.
• [19] Bishop, R.L., There is More Than One Way to Frame a Curve, American Mathematical Monthly, 82 (1975), no. 3, 246-251.
• [20] Hanson, A.J., and Ma, H., Quaternion Frame Approach to Streamline Visualization, IEEE Transactions on Visulation and Computer Graphics, 1 (1995), no.2, 164-174.
• [21] B. Bükçü and M.K. Karacan, Bishop frame of the spacelike curve with a spacelike principal normal in Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Series A1, 57 (2008), no. 1, 13-22.
• [22] B. Bükçü and M.K. Karacan, Bishop frame of the spacelike curve with a spacelike binormal in Minkowski 3-space, Selçuk J. Appl. Math, 11 (2010), no. 1, 15-25.
• [23] Bükçü, B. and Karacan, M.K., The Slant Helices according to Bishop Frame of the Spacelike Curve in Lorentzian Space, Journal of Interdisciplinary Mathematics, 12 (2009), no. 5, 691- 700.