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Euclidean Curves with Incompressible Canonical Vector Field

Year 2018, Volume: 8 Issue: 2, 70 - 82, 28.12.2018

Kadri Arslan , Yılmaz Aydın Eray Demirbaş Aziz Yazla

https://izlik.org/JA77ZU42WK

Abstract

In
the present study we consider Euclidean curves with incompressible canonical
vector fields. We investigate such curves in terms of their curvature
functions. Recently, B.Y. Chen gave classification of plane curves with
incompressible canonical vector fields. For higher dimensional case we gave a
complete classification of Euclidean space curves with incompressible canonical
vector fields. Further we obtain some results of the Euclidean curves with incompressible
canonical vector fields in -dimensional Euclidean space E4.

Keywords

Generalized helix Salkowski curve Regular curve Canonical vector field

References

  • [1] A. T. Ali, Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space, Mathematica Aeterna, 1(2011), 201 - 210.
  • [2] B. Y. Chen, Euclidean submanifolds with incompressible canonical vector field, arXiv:1801.07196v3 [math.DG] 29 Jan 2018.
  • [3] J. W. Bruce, P. J. Giblin, Curves and Singularities, A Geometrical Introduction to Singularity Theory, Second edition, Cambridge University Press, Cambridge, 1992.
  • [4] H. Gluck, Higher curvatures of curves in Euclidean space, Am. Math. Monthly 73 (1966), 699-704.
  • [5] F. Klein and S. Lie, Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen Transformationen in sich übergehen, Math. Ann. 4 (1871), 50-84.
  • [6] J. Monterde, Curves with constant curvature ratios, Bull. Mexican Math. Soc. Ser. 3A 13(1) (2007), 177-186.
  • [7] G. Öztürk, K. Arslan and H. H. Hacisalihoglu, A characterization of ccr-curves in R^{m}, Proc. Estonian Acad. Sci. 57(4) (2008), 217-224.
  • [8] G. Öztürk, S. Gürpınar and K. Arslan, A New Characterization of Curves in Euclidean 4-Space E⁴, Bull. Acad. Stiinte a Republicii Moldova Mathematica, 83(2017), 39-50.
  • [9] E. Salkowski, Zur transformation von raumkurven, Math. Ann. 66(4) (1909), 517-557.

Year 2018, Volume: 8 Issue: 2, 70 - 82, 28.12.2018

Kadri Arslan , Yılmaz Aydın Eray Demirbaş Aziz Yazla

https://izlik.org/JA77ZU42WK

Abstract

References

  • [1] A. T. Ali, Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space, Mathematica Aeterna, 1(2011), 201 - 210.
  • [2] B. Y. Chen, Euclidean submanifolds with incompressible canonical vector field, arXiv:1801.07196v3 [math.DG] 29 Jan 2018.
  • [3] J. W. Bruce, P. J. Giblin, Curves and Singularities, A Geometrical Introduction to Singularity Theory, Second edition, Cambridge University Press, Cambridge, 1992.
  • [4] H. Gluck, Higher curvatures of curves in Euclidean space, Am. Math. Monthly 73 (1966), 699-704.
  • [5] F. Klein and S. Lie, Uber diejenigen ebenenen kurven welche durch ein geschlossenes system von einfach unendlich vielen vartauschbaren linearen Transformationen in sich übergehen, Math. Ann. 4 (1871), 50-84.
  • [6] J. Monterde, Curves with constant curvature ratios, Bull. Mexican Math. Soc. Ser. 3A 13(1) (2007), 177-186.
  • [7] G. Öztürk, K. Arslan and H. H. Hacisalihoglu, A characterization of ccr-curves in R^{m}, Proc. Estonian Acad. Sci. 57(4) (2008), 217-224.
  • [8] G. Öztürk, S. Gürpınar and K. Arslan, A New Characterization of Curves in Euclidean 4-Space E⁴, Bull. Acad. Stiinte a Republicii Moldova Mathematica, 83(2017), 39-50.
  • [9] E. Salkowski, Zur transformation von raumkurven, Math. Ann. 66(4) (1909), 517-557.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Kadri Arslan

Yılmaz Aydın This is me

Eray Demirbaş This is me

Aziz Yazla This is me

Submission Date May 30, 2018
Acceptance Date January 1, 2019
Publication Date December 28, 2018
IZ https://izlik.org/JA77ZU42WK
Published in Issue Year 2018 Volume: 8 Issue: 2

Cite

APA Arslan, K., Aydın, Y., Demirbaş, E., & Yazla, A. (2018). Euclidean Curves with Incompressible Canonical Vector Field. Adıyaman University Journal of Science, 8(2), 70-82. https://izlik.org/JA77ZU42WK
AMA 1.Arslan K, Aydın Y, Demirbaş E, Yazla A. Euclidean Curves with Incompressible Canonical Vector Field. ADYU J SCI. 2018;8(2):70-82. https://izlik.org/JA77ZU42WK
Chicago Arslan, Kadri, Yılmaz Aydın, Eray Demirbaş, and Aziz Yazla. 2018. “Euclidean Curves With Incompressible Canonical Vector Field”. Adıyaman University Journal of Science 8 (2): 70-82. https://izlik.org/JA77ZU42WK.
EndNote Arslan K, Aydın Y, Demirbaş E, Yazla A (December 1, 2018) Euclidean Curves with Incompressible Canonical Vector Field. Adıyaman University Journal of Science 8 2 70–82.
IEEE [1]K. Arslan, Y. Aydın, E. Demirbaş, and A. Yazla, “Euclidean Curves with Incompressible Canonical Vector Field”, ADYU J SCI, vol. 8, no. 2, pp. 70–82, Dec. 2018, [Online]. Available: https://izlik.org/JA77ZU42WK
ISNAD Arslan, Kadri - Aydın, Yılmaz - Demirbaş, Eray - Yazla, Aziz. “Euclidean Curves With Incompressible Canonical Vector Field”. Adıyaman University Journal of Science 8/2 (December 1, 2018): 70-82. https://izlik.org/JA77ZU42WK.
JAMA 1.Arslan K, Aydın Y, Demirbaş E, Yazla A. Euclidean Curves with Incompressible Canonical Vector Field. ADYU J SCI. 2018;8:70–82.
MLA Arslan, Kadri, et al. “Euclidean Curves With Incompressible Canonical Vector Field”. Adıyaman University Journal of Science, vol. 8, no. 2, Dec. 2018, pp. 70-82, https://izlik.org/JA77ZU42WK.
Vancouver 1.Kadri Arslan, Yılmaz Aydın, Eray Demirbaş, Aziz Yazla. Euclidean Curves with Incompressible Canonical Vector Field. ADYU J SCI [Internet]. 2018 Dec. 1;8(2):70-82. Available from: https://izlik.org/JA77ZU42WK

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