DOI QR코드

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CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE

  • Ucum, Ali (Department of Mathematics, Faculty of Science and Arts, University of Kirikkale) ;
  • Ilarslan, Kazim (Department of Mathematics, Faculty of Science and Arts, University of Kirikkale) ;
  • Karakus, Siddika Ozkaldi (Department of Mathematics, Faculty of Sciences and Arts, Bilecik Seyh Edebali University)
  • 투고 : 2014.04.16
  • 심사 : 2014.06.18
  • 발행 : 2014.09.25

초록

In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

키워드

참고문헌

  1. Chen, B. Y., When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110 (2003), 147-152. https://doi.org/10.2307/3647775
  2. Chen, B. Y. and Dillen, F., Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica 33(2) (2005), 77-90.
  3. Izumiya, S. and Takeuchi, N., New special curves and developable surfaces, Turkish J. Math. 28(2) (2004), 153-163.
  4. O'Neill, B., Semi-Riemannian Differential Geometry, Academic Press, New York, 1983.
  5. Ozkaldi Karakus S., Ilarslan K. and Yayli, Y., A new approach for character-ization of curve couples in Euclidean 3-space, Honam Mathematical J. 36(1) (2014), 113-129. https://doi.org/10.5831/HMJ.2014.36.1.113
  6. Kuhnel, W., Differential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden, 1999.
  7. Liu, H. andWang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88 (2008), 120-126. https://doi.org/10.1007/s00022-007-1949-0
  8. Millman, R. S. and Parker, G. D., Elements of differential geometry, Prentice-Hall, New Jersey, 1977.