Some characterizations of curves of AW(k)-type in the Bishop frame

Abstract

In this paper, we consider curves of AW(k)-type with harmonic curvatures in the Bishop frame in Euclidean space. Moreover,we obtain slant helices of AW(k)-type according to the Bishop frame in Euclidean space

Keywords

• Bishop frame,Frenet frame,AW(k)-type,harmonic curvature,slant helices

Some characterizations of curves of AW(k)-type according to the Bishop frame

Abstract

References

1. K. Arslan and A. West, Product submanifolds with pointwise 3-planar normal sections, Glasgow Math. J., 37, 73-81, (1995).
2. K. Arslan and C. ¨Ozg¨ur, Curves and surfaces of AW (k)-type, Geometry and Topology of Submanifolds IX, World Scientific, 21-26, (1997).
3. K. Arslan, Y. C¸ elik and H. H. Hacısalihoglu, On harmonic curvatures of Frenet curve, Commum. Fac. Sci. Univ. Ank. Series A1, 49, 15-23, (2000).
4. L. R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly, 82(3), 246-251, (1975).
5. B. Bukcu and M. K. Karacan, The slant helices according to Bishop frame, World Academy of Science, Engineering and Technology, 59, 1039-1042, (2009).
6. C¸ . Camcı, L. Kula and M. Altınok, On spherical slant helices in Euclidean 3-space, arXiv: 1308.5532v3, (2013).
7. M. K. Karacan and B. Bukcu, On natural curvatures of Bishop frame, Journal of Vectorial Relativity, 5, 34-41, (2010).
8. B. Kılıc and K. Arslan, On curves and surfaces of AW (k)-type, BAU Fen Bil. Enst. Dergisi, 6(1), 52-61, (2004).

9. ˙I. Kisi and G. ¨Ozt¨urk, AW (k)-type curves according to the Bishop frame, arXiv: 1305.3381, (2013).
10. C. ¨Ozg¨ur and F. Gezgin, On some curves of AW (k)-type, Differential Geometry-Dynamical Systems, 7, 74-80, (2005).
11. D. ¨Unal, ˙I. Kisi and M. Tosun, Spinor Bishop equations of curves in Euclidean 3-space, Advances in Applied Clifford Algebras, 23(3), 757-765, (2013).
12. H.H. Hacısalihoglu, Diferensiyel Geometri, ˙In¨on¨u ¨Universitesi Yayınları, Malatya, (1995).
13. A. Sabuncuoglu, Diferensiyel Geometri, Nobel Yayınları, Ankara, (2004).