The explicit determinations of dual plane curves and dual helices in terms of its dual curvature and dual torsion

• Autorzy: Lee J. W. , Choi J.H. , Jin D. H.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we give the explicit determinations of dual plane curves, general dual helices and dual slant helices in terms of its dual curvature and dual torsion as a fundamental theory of dual curves in a dual 3-space.

Słowa kluczowe

EN

dual curve; slant helix; dual slant helix; dual curvature; dual torsion

PL

podwójna krzywa; skok helisy; podwójny skok helisy; podwójna krzywizna; podwójne skręcanie

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 1
• Strony: 156--169
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Lee J. W.

• Department of Mathematics, University of Missouri 202 Math. Sci. Bldg., Columbia MO 65211, U.S.A.

autor

Choi J.H.

• Department of Mathematics, University of Ulsan Daehawkro 102, Moogeodong, Ulsan City, Korea

autor

Jin D. H.

• Department of Mathematics, Dongguk University, Gyeongju 780-714, Korea

Bibliografia

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• [2] J. H. Choi, Y. H. Kim, Some associated curves of a Frenet curve and its applications, preprint (2010).
• [3] M. A. Gungor, M. Tosun, A study on dual Mannheim partner curves, Int. Math. Forum 5(47) (2010), 2319–2330.
• [4] S. Izumiya, N. Takeuchi, New special curves and developable surfaces, Turk. J. Math. 28 (2004), 531–537.
• [5] J. W. Lee, J. H. Choi, D. H. Jin, Slant dual Mannheim partner curves in the dual space D3, Int. J. Contemp. Math. Sciences 6(3) (2011), 1535–1544.
• [6] Ö. Köse, S. Nizamoglu, M. Sezer, An explicit characterization of dual spherical curves, Doga Mat. 12(3) (1988), 105–113.
• [7] S. Özkaldi, K. Ilarslan, Y. Yayli, On Mannheim partner curve in dual space, An. St. Univ. Ovidius Constanta 17(2) (2009), 131–142.
• [8] A. Yücesan, N. Ayyıldız, A. C. Çöken, On rectifying dual space curves, Rev. Mat. Complut. 20(2) (2007), 497–506.