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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 512020, 12 pages
Singularities of a Space Curve according to the Relatively Parallel Adapted Frame and Its Visualization
1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Science, Mudanjiang Normal University, Mudanjiang 15701, China
Received 21 October 2012; Accepted 26 December 2012
Academic Editor: Kue-Hong Chen
Copyright © 2013 Haiming Liu and Donghe Pei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. L. Bishop, “There is more than one way to frame a curve,” The American Mathematical Monthly, vol. 82, no. 3, pp. 246–251, 1975.
- B. Bukcu and M. K. Karacan, “Special Bishop motion and Bishop Darboux rotation axis of the space curve,” Journal of Dynamical Systems and Geometric Theories, vol. 6, no. 1, pp. 27–34, 2008.
- B. Bukcu and M. K. Karacan, “The slant helices according to Bishop frame,” International Journal of Computational and Mathematical Sciences, vol. 3, no. 2, pp. 67–70, 2009.
- L. Kula and Y. Yayli, “On slant helix and its spherical indicatrix,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 600–607, 2005.
- S. Yılmaz, E. Özyılmaz, and M. Turgut, “New spherical indicatrices and their characterizations,” Analele Ştiinţifice ale Universităţii Ovidius Constanţa, vol. 18, no. 2, pp. 337–353, 2010.
- L. Kula, N. Ekmekci, Y. Yaylı, and K. İlarslan, “Characterizations of slant helices in Euclidean 3-space,” Turkish Journal of Mathematics, vol. 34, no. 2, pp. 261–273, 2010.
- S. Yılmaz and M. Turgut, “A new version of Bishop frame and an application to spherical images,” Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 764–776, 2010.
- B. Bükcü and M. K. Karacan, “The bishop darboux rotation axis of the spacelike curve in minkowski 3-space,” Journal of the Faculty of Science, Ege University, vol. 3, no. 1, pp. 1–5, 2007.
- M. K. Karacan and B. Bukcu, “An alternative moving frame for tubular surfaces around timelike curves in the Minkowski 3-space,” Balkan Journal of Geometry and Its Applications, vol. 12, no. 2, pp. 73–80, 2007.
- M. K. Karacan, B. Bukcu, and N. Yuksel, “On the dual Bishop Darboux rotation axis of the dual space curve,” Applied Sciences, vol. 10, pp. 115–120, 2008.
- C. Y. Han, “Nonexistence of rational rotation-minimizing frames on cubic curves,” Computer Aided Geometric Design, vol. 25, no. 4-5, pp. 298–304, 2008.
- N. Clauvelin, W. K. Olson, and I. Tobias, “Characterization of the geometry and topology of DNA pictured as a discrete collection of atoms,” Journal of Chemical Theory Computation, vol. 8, pp. 1092–1107, 2012.
- K. Shoeemake, “Animating rotation with quaternion curves,” in Computer Graphics, vol. 19 of Proceedings of Siggapo, pp. 245–254, 1985.
- A. J. Hanson and H. Ma, “Parallel transport approach to curve framing,” Tech. Rep. TR 425, pp. 3–7, Indiana University, 1995.
- J. W. Bruce and P. J. Giblin, Curves and Singularities, Cambridge University Press, Glasgow, UK, 2nd edition, 1992.
- J. W. Bruce and P. J. Giblin, “Generic geometry,” The American Mathematical Monthly, vol. 90, no. 8, pp. 529–545, 1983.
- S. Izumiya, H. Katsumi, and T. Yamasaki, The Rectifying Developable and the Spherical Darboux Image of a Space Curve, vol. 50 of Banach Center Publications, Polish Academy of Science, Warsaw, Poland, 1999.
- Z. Wang and D. Pei, “Null Darboux developable and pseudo-spherical Darboux image of null Cartan curve in Minkowski 3-space,” Hokkaido Mathematical Journal, vol. 40, no. 2, pp. 219–240, 2011.
- S. Izumiya, D. Pei, and T. Sano, “The lightcone Gauss map and the lightcone developable of a spacelike curve in Minkowski 3-space,” Glasgow Mathematical Journal, vol. 42, no. 1, pp. 75–89, 2000.