Yıl: 2004 Cilt: 28 Sayı: 2 Sayfa Aralığı: 153 - 163 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

New special curves and developable surfaces

Öz:
We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylindrical helices. One of the results in this paper gives a classification of special developable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are straight forward and classical. However, there have been no papers which have investigated slant helices and conical geodesic curves so far as we know.
Anahtar Kelime:

Konular: Matematik
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] J.W. Bruce and P.J.Giblin. Curves and Singularities, 2nd. ed. Cambridge Univ. Press, Cambridge, (1992).
  • [2] M. do Carmo. Differential Geometry of Curves and Surfaces. Prentice-Hall, New Jersey (1976).
  • [3] S. Izumiya, H. Katsumi and T. Yamasaki. The rectifying developable and the spherical Darboux image of a space curve. Geometry and topology of caustics-Caustics '98- Banach Center Publications, 50 pp. 137-149 (1999) .
  • [4] S. Izumiya and N. Takeuchi. Special curves and ruled surfaces. Applicable Mathematics in the Golden Age (ed., J.C. Misra), Narosa Publishing House, New Delhi, 305-338 (2003).
  • [5] S. Izumiya and N. Takeuchi. Generic properties of helices and Bertrand curves, to appear in Journal of Geometry.
  • [6] S. Izumiya and N. Takeuchi Geometry of ruled surfaces. Applicable Mathematics in the Golden Age (ed., J.C. Misra), Narosa Publishing House, New Delhi, 305-338 (2003).
  • [7] O. P. Shcherbak, Protectively dual space curve and Legendre singularities. Sel. Math. Sov., 5 pp. 391-421 (1986).
  • [8] J. Koenderink. Solid shape. MIT Press, Cambridge, MA, (1990).
APA IZUMIYA S, TAKEUCHI N (2004). New special curves and developable surfaces. , 153 - 163.
Chicago IZUMIYA Shyuichi,TAKEUCHI Nobuko New special curves and developable surfaces. (2004): 153 - 163.
MLA IZUMIYA Shyuichi,TAKEUCHI Nobuko New special curves and developable surfaces. , 2004, ss.153 - 163.
AMA IZUMIYA S,TAKEUCHI N New special curves and developable surfaces. . 2004; 153 - 163.
Vancouver IZUMIYA S,TAKEUCHI N New special curves and developable surfaces. . 2004; 153 - 163.
IEEE IZUMIYA S,TAKEUCHI N "New special curves and developable surfaces." , ss.153 - 163, 2004.
ISNAD IZUMIYA, Shyuichi - TAKEUCHI, Nobuko. "New special curves and developable surfaces". (2004), 153-163.
APA IZUMIYA S, TAKEUCHI N (2004). New special curves and developable surfaces. Turkish Journal of Mathematics, 28(2), 153 - 163.
Chicago IZUMIYA Shyuichi,TAKEUCHI Nobuko New special curves and developable surfaces. Turkish Journal of Mathematics 28, no.2 (2004): 153 - 163.
MLA IZUMIYA Shyuichi,TAKEUCHI Nobuko New special curves and developable surfaces. Turkish Journal of Mathematics, vol.28, no.2, 2004, ss.153 - 163.
AMA IZUMIYA S,TAKEUCHI N New special curves and developable surfaces. Turkish Journal of Mathematics. 2004; 28(2): 153 - 163.
Vancouver IZUMIYA S,TAKEUCHI N New special curves and developable surfaces. Turkish Journal of Mathematics. 2004; 28(2): 153 - 163.
IEEE IZUMIYA S,TAKEUCHI N "New special curves and developable surfaces." Turkish Journal of Mathematics, 28, ss.153 - 163, 2004.
ISNAD IZUMIYA, Shyuichi - TAKEUCHI, Nobuko. "New special curves and developable surfaces". Turkish Journal of Mathematics 28/2 (2004), 153-163.