Curves of constant breadth according to Darboux frame

Year 2017, Volume: 66 Issue: 2, 44 - 52, 01.08.2017

Bülent Altunkaya Ferdag Kahraman Aksoyak

https://doi.org/10.1501/Commua1_0000000799

Cited By: 2

Abstract

In this paper, we investigate constant breadth curves on a surfaceaccording to Darboux frame and give some characterizations of these curves

Keywords

Darboux frame, constant breadth curve, Euclidean space

References

• Akdo¼gan Z., Ma¼gden A., Some characterizations of curves of constant breadth in Enspace, Turk. J. Math., 25, 433-444, 2001.
• Ball, N.H., On ovals, American Mathematical Monthly, 37(3), 348-353, 1930.
• Euler L., De curvis triangularibus, Acta Acad. Petropol, 3-30, 1778.
• Fujiwara M., On space curves of constant breadth, Tohoku Math. J., 5, 179-184,1914.
• Kocayi¼git H., Önder, M., Space curves of constant breadth in Minkowski 3-space, Annali di Mathematica 192, 805–814, 2013.
• Köse Ö., Some properties of ovals and curves of constant width in a plane, Do¼ga Math. 8, 126, 1984.
• Köse Ö., On space curves of constant breadth, Do¼ga Math. 10, 11-14, 1986.
• Ma¼gden A. Köse Ö., On the curves of constant breadth in E4space, Turk. J. Math., 21, 284, 1997.
• Mellish, A.P., Notes on diğerential geometry, Annals of Math., 32(1), 181-190, 1931.
• Önder M., Kocayi¼git H., Candan E. Diğerential equations characterizing timelike and space- like curves of constant breadth in Minkowski 3-space E1, J. Korean Math. Soc. 48(4), 849-866, Sabuncuo¼glu A., Diğerential Geometry, Nobel Press, Ankara, 2006.
• Struik, D.J., Diğerential geometry in the large, Bulletin Amer. Math. Soc., 37, 49-62, 1931.
• Yılmaz S., Turgut M., On the timelike curves of constant breadth in Minkowski 3-space, International J. Math. Combin 3, 34-39, 2008.
• Current address : Ahi Evran University, Division of Elementary Mathematics Education, Kır¸se- hir, TURKEY E-mail address, B. Altunkaya: [e-mail] E-mail address, F. Kahraman Aksoyak: [e-mail]