Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space

Space Curves of Constant Breadth according to Bishop Frame in Euclidean 3-Space

In this paper, space curves of constant breadth according to Bishop frame in Euclidean 3-space are studied. It is shown that in some special cases, space curves of constant breadth are slant helix. Moreover, the differential equations characterizing the space curves of constant breadth in E are given. 3 are given

___

  • Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • Ball, N.H., On ovals, American Mathematical Monthly, 37(7) : 348-353, 1930.
  • Barbier, E., Note sur le probléme de I’aiguille et le jeu du joint couvert, Journal de mathématiques pures et appliquées, 2(5) : 273-286, 1860.
  • Blaschke, W., Leibziger Berichte, 67 : 290, 1917.
  • Mellish, A.P., Notes on Differential Geometry, Annals of Mathematics, 32(1) : 181-190, 1931.
  • Fujiwara, M., On Space Curves of Constant Breadth, Tohoku Mathematical Journal, 5 : 180-184, 1914.
  • Hammer, P.C., Constant Breadth Curves in the Plane, Procedings of the American Mathematical Society, 6(2) : 333-334, 1955.
  • Smakal, S., Curves of Constant Breadth, Czechoslovak Mathematical Journal, 23(1) : 86-94, 1973.
  • Köse, Ö., Düzlemde Ovaller ve Sabit Genişlikli Eğrilerin Bazı Özellikleri, Doğa Bilim Dergisi, Seri B, 8(2) : 119-126, 1984.
  • Reuleaux, F., The Kinematics of Machinery, Translated by A. B. W. Kennedy, Dover Pub. New York, 1963.
  • Köse, Ö., On Space Curves of Constant Breadth, Doğa Tr. J. Math, 10(1) : 11-14, 1986.
  • Sezer, M., Differential Equations Characterizing Space Curves of Constant Breadth and a Criterion
  • for These Curves, Turkish J. of Math, 13(2) : 70-78, 1989.
  • Akdoğan, Z., and Mağden, A., Some Characterization of Curves of Constant Breadth in E Space,
  • Turk J Math, 25 : 433-444, 2001.
  • Mağden, A., and Köse, Ö., On the Curves of Constant Breadth in E Space, Tr. J. of Mathematics, 21 277-284, 1997.
  • Önder, M., Kocayiğit, H. and Candan, E., Differential Equations Characterizing Timelike and
  • Spacelike Curves of Constant Breadth in Minkowski 3-Space 1 3 866, 2011.
  • Kocayiğit, H. and Önder, M., Space Curves of Constant Breadth in Minkowski 3-Space, Annali di
  • Matematica, 192(5) : 805-814, 2013.
  • Hanson, A.J. and Ma, H., Parallel Transport Approach to Curve Framing, Indiana University,
  • Technical Report TR425, January 11, 1995.
  • Bishop, R.L., There is More Than One Way to Frame a Curve, American Mathematical Monthly, 82(3) : 246-251, 1975.
  • Hanson, A.J., and Ma, H., Quaternion Frame Approach to Streamline Visualization, IEEE
  • Transactions on Visulation and Computer Graphics, 1(2) : 164-174, 1995.
  • Bükcü, B. and Karacan, M.K., The Slant Helices according to Bishop Frame, World Academy of
  • Science, Engineering and Technology, 3(11) : 853-856, 2009.