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Euclidean Curves with Incompressible Canonical Vector Field

Yıl 2018, Cilt: 8 Sayı: 2, 70 - 82, 28.12.2018

Kadri Arslan Yılmaz Aydın Eray Demirbaş Aziz Yazla

Öz

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.

Anahtar Kelimeler

Generalized helix Salkowski curve Regular curve Canonical vector field

Kaynakça

  • [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.

Yıl 2018, Cilt: 8 Sayı: 2, 70 - 82, 28.12.2018

Kadri Arslan Yılmaz Aydın Eray Demirbaş Aziz Yazla

Öz

Kaynakça

  • [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.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Matematik
Yazarlar

Kadri Arslan

Yılmaz Aydın Bu kişi benim

Eray Demirbaş Bu kişi benim

Aziz Yazla Bu kişi benim

Yayımlanma Tarihi 28 Aralık 2018
Gönderilme Tarihi 30 Mayıs 2018
Kabul Tarihi 1 Ocak 2019
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 2

Kaynak Göster

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.
AMA Arslan K, Aydın Y, Demirbaş E, Yazla A. Euclidean Curves with Incompressible Canonical Vector Field. ADYU J SCI. Aralık 2018;8(2):70-82.
Chicago Arslan, Kadri, Yılmaz Aydın, Eray Demirbaş, ve Aziz Yazla. “Euclidean Curves With Incompressible Canonical Vector Field”. Adıyaman University Journal of Science 8, sy. 2 (Aralık 2018): 70-82.
EndNote Arslan K, Aydın Y, Demirbaş E, Yazla A (01 Aralık 2018) Euclidean Curves with Incompressible Canonical Vector Field. Adıyaman University Journal of Science 8 2 70–82.
IEEE K. Arslan, Y. Aydın, E. Demirbaş, ve A. Yazla, “Euclidean Curves with Incompressible Canonical Vector Field”, ADYU J SCI, c. 8, sy. 2, ss. 70–82, 2018.
ISNAD Arslan, Kadri vd. “Euclidean Curves With Incompressible Canonical Vector Field”. Adıyaman University Journal of Science 8/2 (Aralık 2018), 70-82.
JAMA 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 vd. “Euclidean Curves With Incompressible Canonical Vector Field”. Adıyaman University Journal of Science, c. 8, sy. 2, 2018, ss. 70-82.
Vancouver Arslan K, Aydın Y, Demirbaş E, Yazla A. Euclidean Curves with Incompressible Canonical Vector Field. ADYU J SCI. 2018;8(2):70-82.
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