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

Year 2014, Volume: 2 Issue: 3, 206 - 213, 01.12.2014

Yasin Unluturk

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

References

  • K. Arslan and A. West, Product submanifolds with pointwise 3-planar normal sections, Glasgow Math. J., 37, 73-81, (1995).
  • K. Arslan and C. ¨Ozg¨ur, Curves and surfaces of AW (k)-type, Geometry and Topology of Submanifolds IX, World Scientific, 21-26, (1997).
  • 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).
  • L. R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly, 82(3), 246-251, (1975).
  • B. Bukcu and M. K. Karacan, The slant helices according to Bishop frame, World Academy of Science, Engineering and Technology, 59, 1039-1042, (2009).
  • C¸ . Camcı, L. Kula and M. Altınok, On spherical slant helices in Euclidean 3-space, arXiv: 1308.5532v3, (2013).
  • M. K. Karacan and B. Bukcu, On natural curvatures of Bishop frame, Journal of Vectorial Relativity, 5, 34-41, (2010).
  • B. Kılıc and K. Arslan, On curves and surfaces of AW (k)-type, BAU Fen Bil. Enst. Dergisi, 6(1), 52-61, (2004).
  • ˙I. Kisi and G. ¨Ozt¨urk, AW (k)-type curves according to the Bishop frame, arXiv: 1305.3381, (2013).
  • C. ¨Ozg¨ur and F. Gezgin, On some curves of AW (k)-type, Differential Geometry-Dynamical Systems, 7, 74-80, (2005).
  • 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).
  • H.H. Hacısalihoglu, Diferensiyel Geometri, ˙In¨on¨u ¨Universitesi Yayınları, Malatya, (1995).
  • A. Sabuncuoglu, Diferensiyel Geometri, Nobel Yayınları, Ankara, (2004).

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

Year 2014, Volume: 2 Issue: 3, 206 - 213, 01.12.2014

Yasin Unluturk

Abstract

References

  • K. Arslan and A. West, Product submanifolds with pointwise 3-planar normal sections, Glasgow Math. J., 37, 73-81, (1995).
  • K. Arslan and C. ¨Ozg¨ur, Curves and surfaces of AW (k)-type, Geometry and Topology of Submanifolds IX, World Scientific, 21-26, (1997).
  • 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).
  • L. R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly, 82(3), 246-251, (1975).
  • B. Bukcu and M. K. Karacan, The slant helices according to Bishop frame, World Academy of Science, Engineering and Technology, 59, 1039-1042, (2009).
  • C¸ . Camcı, L. Kula and M. Altınok, On spherical slant helices in Euclidean 3-space, arXiv: 1308.5532v3, (2013).
  • M. K. Karacan and B. Bukcu, On natural curvatures of Bishop frame, Journal of Vectorial Relativity, 5, 34-41, (2010).
  • B. Kılıc and K. Arslan, On curves and surfaces of AW (k)-type, BAU Fen Bil. Enst. Dergisi, 6(1), 52-61, (2004).
  • ˙I. Kisi and G. ¨Ozt¨urk, AW (k)-type curves according to the Bishop frame, arXiv: 1305.3381, (2013).
  • C. ¨Ozg¨ur and F. Gezgin, On some curves of AW (k)-type, Differential Geometry-Dynamical Systems, 7, 74-80, (2005).
  • 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).
  • H.H. Hacısalihoglu, Diferensiyel Geometri, ˙In¨on¨u ¨Universitesi Yayınları, Malatya, (1995).
  • A. Sabuncuoglu, Diferensiyel Geometri, Nobel Yayınları, Ankara, (2004).
There are 13 citations in total.

Details

Journal Section Articles
Authors

Yasin Unluturk This is me

Publication Date December 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 3

Cite

APA Unluturk, Y. (2014). Some characterizations of curves of AW(k)-type according to the Bishop frame. New Trends in Mathematical Sciences, 2(3), 206-213.
AMA Unluturk Y. Some characterizations of curves of AW(k)-type according to the Bishop frame. New Trends in Mathematical Sciences. December 2014;2(3):206-213.
Chicago Unluturk, Yasin. “Some Characterizations of Curves of AW(k)-Type According to the Bishop Frame”. New Trends in Mathematical Sciences 2, no. 3 (December 2014): 206-13.
EndNote Unluturk Y (December 1, 2014) Some characterizations of curves of AW(k)-type according to the Bishop frame. New Trends in Mathematical Sciences 2 3 206–213.
IEEE Y. Unluturk, “Some characterizations of curves of AW(k)-type according to the Bishop frame”, New Trends in Mathematical Sciences, vol. 2, no. 3, pp. 206–213, 2014.
ISNAD Unluturk, Yasin. “Some Characterizations of Curves of AW(k)-Type According to the Bishop Frame”. New Trends in Mathematical Sciences 2/3 (December 2014), 206-213.
JAMA Unluturk Y. Some characterizations of curves of AW(k)-type according to the Bishop frame. New Trends in Mathematical Sciences. 2014;2:206–213.
MLA Unluturk, Yasin. “Some Characterizations of Curves of AW(k)-Type According to the Bishop Frame”. New Trends in Mathematical Sciences, vol. 2, no. 3, 2014, pp. 206-13.
Vancouver Unluturk Y. Some characterizations of curves of AW(k)-type according to the Bishop frame. New Trends in Mathematical Sciences. 2014;2(3):206-13.