ON CURVES OF CONSTANT BREADTH IN G13

In this work, dierential equations characterizing curves of constant breadth have been given in pseudo-Galilean space G13 : The special cases related to these dierential equations have been studied in G13.

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  • [1] Akdogan,Z. and Ma˘gden,A., (2001), Some characterizations of curves of constant breadth in En space, Turk. J. Math., 25, pp. 433-444.
  • [2] Ball,N.H., (1930), On ovals, Amer. Math. Month., 27, pp. 348-353.
  • [3] Blaschke,W., (1915), Konvexe bereiche gegebener konstanter breite und kleinsten inhalts, Math. Ann., 76, pp. 504-513.
  • [4] Divjak,B., (1998), Curves in pseudo-Galilean geometry. Annales Univ. Budapest, 41, pp. 117-128.
  • [5] Erjavec,Z. and Divjak,B., (2008), The equiform differential geometry of curves in the pseudo-Galilean space, Math. Comm.,13, pp. 321-332.
  • [6] Euler,L., (1780), De curvis triangularibus, Acta Acad. Prtropol., 1778, pp. 3-30.
  • [7] Fujivara,M., (1914), On space curves of constant breadth. Tohoku Math. J., 5, pp. 179-184.
  • [8] K¨ose,O., (1984), Some properties of ovals and curves of constant width in a plane. Do˘ga Math., ¨ 8:119-126.
  • [9] K¨ose,O., (1986), On space curves of constant breadth. Do˘ga Math., 10:11-14. ¨
  • [10] Ma˘gden,A. and K¨ose,O., (1997), On the curves of constant breadth in ¨ E 4 space. Turk. J. Math., 21, pp. 227-284.
  • [11] Reuleaux,F., (1963), The Kinematics of Machinery, trans. A. Kennedy, Dover, New York (reprint of 1876 translation of 1875 German original).
  • [12] Yılmaz,S., Savci,U.Z. and Turgut,M., (2014), Characterizations of curves of constant breadth in ¨ Galilean 3-space G 3, J. of Adv. Res. Pure Math., 6 (1), pp. 19-24