Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

A NEW APPROACH FOR CHARACTERIZATION OF CURVE COUPLES IN EUCLIDEAN 3-SPACE

  • Karakus, Siddika Ozkaldi (Department of Mathematics, Faculty of Sciences and Arts, Bilecik Seyh Edebali University) ;
  • Ilarslan, Kazim (Department of Mathematics, Faculty of Science and Arts, University of Kirikkale) ;
  • Yayli, Yusuf (Department of Mathematics, Faculty of Science, University of Ankara)
  • Received : 2013.12.13
  • Accepted : 2014.01.24
  • Published : 2014.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any 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.

Keywords

References

  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. Kuhnel, W., Differential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden, 1999.
  5. Liu, H. and Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88 (2008), 120-126. https://doi.org/10.1007/s00022-007-1949-0
  6. Millman, R. S. and Parker, G. D., Elements of differential geometry, Prentice-Hall, New Jersey, 1977.

Cited by

  1. CURVE COUPLES AND SPACELIKE FRENET PLANES IN MINKOWSKI 3-SPACE vol.36, pp.3, 2014, https://doi.org/10.5831/HMJ.2014.36.3.475