ON CURVES OF CONSTANT WIDTH DUE TO THE BISHOP FRAME OF TYPE-2 IN DUAL EUCLIDEAN SPACE D^3

Abstract

In this work, we study dual constant width curves due to the Bishop frame of type-2 in

dual space 3 D . We obtain a differential equation which characterizes these curves in 𝐷^3. For

special solutions of this differential equation system, we obtain some results in 𝐷^3.

Keywords

• Dual curves,dual constant width curves,dual Bishop frame of type-2,dual Euclidean space

References

1. [1] Bishop, L.R., There is More Than One Way to Frame a Curve, Amer. Math. Monthly 82, 246-251, 1975.
2. [2] Blaschke, W., Konvexe Bereiche Gegebener Konstanter Breite und Kleinsten Inhalts. Math. Ann. 76, 504-513, 1915.
3. [3] Euler, L., De Curvis Trangularibus, Acta Acad Petropol, 1870.
4. [4] Fujivara, M., On Space Curves of Constant Breadth, Tohoku Math. J. 5, 179-184, 1963.
5. [5] Köse, Ö., On Space Curves of Constant Breadth, Doğa Turk. J. Math. 10, 1, 11-14, 1986.
6. [6] Reuleaux, F., The Kinematics of Machinery, Dover Publications, New York, 1963.
7. [7] Veldkamp, G.R., On The Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mech. Math. Theory, 11, 141-156, 1976.
8. [8] Yılmaz, S., Turgut, M., A New version of Bishop Frame and Application to Spherical Images , Journal of Mathematical Analysis and Applications, 371, 764-776, 2010.

9. [9] Yılmaz, S., Savcı, Ü.Z., Dual Curves of Constant Breadth According to Bishop Frame in Dual Euclidean Space, Mathematical Sciences Letters, 1, 1-4 , 2016.
10. [10] Yılmaz, S., Savcı, Ü.Z., and Ünlütürk, Y., On Dual Spacelike Curves Of Constant Breadth In Dual Lorentzian Space D13, New Trends In Mathematical Sciences, 3, 4, 164– 170, 2015.
11. [11] Yılmaz, S., Savcı, Ü.Z., and Ünlütürk, Y., Spacelike Curves of Constant Breadth According to Bishop Frame in Minkowski 3-space, International J. Math. Combin., 4, 4, 1–6, 2014.
12. [12] Mağden, A., Yılmaz, S., On The Curves Of Constant Breadth In Four Dimensional Galilean Space, International Mathematical Forum, 9, 25, 229–1236, 2014.
13. [13] Yılmaz, S., and Turgut, M., Partially Null Curves of Constant Breadth in Semi- Riemannian Space, Modern Applied Science, 3, 3, 60–63, 2009.
14. [14] Yılmaz, S., Savcı, Ü.Z., and Turgut, M., Characterizations of curves of constant breadth in Galilean 3-space G3, Journal of Advanced Research in Pure Mathematics, 6, 1, 19–24, 2014.
15. [15] Yılmaz, S., and Turgut, M., On the Time-like Curves of Constant Breadth in Minkowski 3-Space,” International Journal of Mathematical Combinatorics, 3, 34–39, 2008.