Dual Curves of Constant Breadth in Dual Euclidean Space D^3

Year 2016, Volume: 4 Issue: 3, 99 - 104, 30.09.2016

Huseyin Kocayigit Nihal Erten

Abstract

In this paper, we study dual curves of constant
breadth in dual Euclidean Space . We obtain the differential equations characterizing dual curves of
constant breadth in  and we introduce some special cases
for these dual curves.

Keywords

Dual Euclidean space, dual Frenet frame

References

• Ayyıldız, N., Çöken, A.C., Yücesan, A., A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11(4), 999-1018 (2007).
• Ball, N. H., On Ovals, American Mathematical Monthly, 37(7), 348-353 (1930).
• Barbier, E., Note sur le probleme de l’aiguille et le jeu du joint couvert. J. Math. Pures Appl., II. Ser. 5, 273-286 (1860).
• Blaschke, W., Konvexe bereiche gegebener konstanter breite und kleinsten inhalts, Mathematische Annalen, B. 76(4), 504-513 (1915).
• Blaschke, W., Einige Bemerkungen über Kurven und Flächen konstanter Breite. Ber. Verh. Sächs. Akad. Leipzig, 67, 290-297 (1915).
• Blaschke, W., Differential Geometric and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover, New York, (1945).
• Hacısalihoğlu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Fen-Edb. Fakültesi, (1983)
• Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30 (1778-1780).
• Fujivara, M., On space curves of constant breadth, Tohoku Math., J., 5, 180-184 (1914).
• Kocayiğit, H., Önder, M., Space curves of constant breadth in Minkowski 3-space, Annali di Matematica, 192(5), 805-814, (2013).
• Kazaz, M., Önder, M., Kocayiğit, H., Spacelike curves of constant breadth in Minkowski 4-space, Int. Journal of Math. Analysis, 22(2) 1061-1068 (2008).
• Köse, Ö., On space curves of constant breadth, Doğa Tr. J. Math., 10(1), 11-14, (1986).
• Köse, Ö., Some Properties of Ovals and Curves of Constant Width in a Plane, Doğa Mat., 2 (8) 119-126 (1984).
• Mağden, A., Köse, Ö., On the curves of constant breadth in E^4 space, Turkish J. Math., 21 (3) 277-284 (1997).
• Mellish, A.P., Notes of Differential Geometry, Annals of Mathematics, 32(1), 181-190 (1931).
• Önder, M., Kocayiğit, H., Candan, E., Differential Equations Characterizing Timelike and Spacelike Curves of Constant Breadth in Minkowski 3-Space E_1^3, J. Korean Math. Soc. 48 (4) 849-866 (2011).
• 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).
• Struik, D. J., Differential Geometry in the Large, Bull. Amer. Math. Soc., 37(2), 49-62 (1931).
• Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory, 11(2), 141-156 (1976).
• Yılmaz, S., Time-like Dual Curves of Constant Breadth in Dual Lorentzian Space, IBSU Scientific Journal, 2 (2), 129-136 (2008).