Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 4 Sayı: 4, 258 - 263, 01.12.2021
https://doi.org/10.33401/fujma.992917

Öz

Kaynakça

  • [1] S. Honda, M. Takahashi, Framed curves in the Euclidean space, Adv. Geom., 16 (2016), 265-276.
  • [2] Y. Wang, D. Pei, R. Gao, Generic properties of framed rectifying curves, Mathematics, 7(1) (2019), 37.
  • [3] A. Kızılay, Ö G. Yıldız, O. Z. Okuyucu, Evolution of quaternionic curve in the semi-Euclidean space E4 2 , Math. Meth. Appl. Sci., 44 (2021), 7577–7587, https://doi.org/10.1002/mma.6374.
  • [4] B. Dog˘an Yazıcı, S. Özkaldı Karakuş, M. Tosun, Framed normal curves in Euclidean space, Tbilisi Math. J., (2020), 27-37.
  • [5] B. Dog˘an Yazıcı, S. Özkaldı Karakuş, M. Tosun, On the classification of framed rectifying curves in Euclidean space, Math. Meth. Appl. Sci., (2021), 1-10, https://doi.org/10.1002/mma.7561.
  • [6] C. Özyurt, Singular curves and their properties, Master Thesis, Ankara University, 2021.
  • [7] S. Honda, T. Masatomo, Evolutes of framed immersions in the Euclidean space, Hokkaido Uni. Preprint Ser. Math., 1095 (2016), 1-24.
  • [8] T. Fukunaga, M. Takahashi, Existence and uniqueness for Legendre curves, J. Geom. 104 (2013), 297-307.
  • [9] K. Eren, Ö . G. Yıldız, M. Akyiğit, Tubular surfaces associated with framed base curves in Euclidean 3-space, Math. Meth. Appl. Sci., (2021), 1- 9, https://doi.org/10.1002/mma.7590.
  • [10] B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly, 110 (2003), 147-152.
  • [11] K. Ilarslan, E. Nesovic, Timelike and null normal curves in Minkowski space E3_1 , Indian J. Pure Appl. Math., 35(7) (2004), 881-888.
  • [12] K. Ilarslan, Spacelike Normal Curves in Minkowski Space E3_1 , Turk. J. Math., 29 (2005), 53-63.
  • [13] K. Ilarslan, E. Nesovic, Spacelike and timelike normal curves in Minkowski space-time, Publ. Inst. Math. Belgrade, 85(99) (2009), 111-118.
  • [14] F. Gökçelik, Z. Bozkurt, ˙I. Gök, F. N. Ekmekçi, Y. Yaylı Parallel transport frame in 4-dimensional Euclidean space, Caspian J. Math. Sci., 3 (2014), 91- 103.

On the Framed Normal Curves in Euclidean 4-space

Yıl 2021, Cilt: 4 Sayı: 4, 258 - 263, 01.12.2021
https://doi.org/10.33401/fujma.992917

Öz

In this paper, we introduce the adapted frame of framed curves and we give the relations between the adapted frame and Frenet type frame of the framed curve in four-dimensional Euclidean space. Moreover, we define the framed normal curves in four-dimensional Euclidean space. We obtain some characterizations of framed normal curves in terms of their framed curvature functions. Furthermore, we give the necessary and sufficient condition for a framed curve to be a framed normal curve.


Kaynakça

  • [1] S. Honda, M. Takahashi, Framed curves in the Euclidean space, Adv. Geom., 16 (2016), 265-276.
  • [2] Y. Wang, D. Pei, R. Gao, Generic properties of framed rectifying curves, Mathematics, 7(1) (2019), 37.
  • [3] A. Kızılay, Ö G. Yıldız, O. Z. Okuyucu, Evolution of quaternionic curve in the semi-Euclidean space E4 2 , Math. Meth. Appl. Sci., 44 (2021), 7577–7587, https://doi.org/10.1002/mma.6374.
  • [4] B. Dog˘an Yazıcı, S. Özkaldı Karakuş, M. Tosun, Framed normal curves in Euclidean space, Tbilisi Math. J., (2020), 27-37.
  • [5] B. Dog˘an Yazıcı, S. Özkaldı Karakuş, M. Tosun, On the classification of framed rectifying curves in Euclidean space, Math. Meth. Appl. Sci., (2021), 1-10, https://doi.org/10.1002/mma.7561.
  • [6] C. Özyurt, Singular curves and their properties, Master Thesis, Ankara University, 2021.
  • [7] S. Honda, T. Masatomo, Evolutes of framed immersions in the Euclidean space, Hokkaido Uni. Preprint Ser. Math., 1095 (2016), 1-24.
  • [8] T. Fukunaga, M. Takahashi, Existence and uniqueness for Legendre curves, J. Geom. 104 (2013), 297-307.
  • [9] K. Eren, Ö . G. Yıldız, M. Akyiğit, Tubular surfaces associated with framed base curves in Euclidean 3-space, Math. Meth. Appl. Sci., (2021), 1- 9, https://doi.org/10.1002/mma.7590.
  • [10] B. Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly, 110 (2003), 147-152.
  • [11] K. Ilarslan, E. Nesovic, Timelike and null normal curves in Minkowski space E3_1 , Indian J. Pure Appl. Math., 35(7) (2004), 881-888.
  • [12] K. Ilarslan, Spacelike Normal Curves in Minkowski Space E3_1 , Turk. J. Math., 29 (2005), 53-63.
  • [13] K. Ilarslan, E. Nesovic, Spacelike and timelike normal curves in Minkowski space-time, Publ. Inst. Math. Belgrade, 85(99) (2009), 111-118.
  • [14] F. Gökçelik, Z. Bozkurt, ˙I. Gök, F. N. Ekmekçi, Y. Yaylı Parallel transport frame in 4-dimensional Euclidean space, Caspian J. Math. Sci., 3 (2014), 91- 103.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Mahmut Akyiğit 0000-0002-8398-365X

Önder Gökmen Yıldız 0000-0002-2760-1223

Yayımlanma Tarihi 1 Aralık 2021
Gönderilme Tarihi 8 Eylül 2021
Kabul Tarihi 8 Kasım 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 4 Sayı: 4

Kaynak Göster

APA Akyiğit, M., & Yıldız, Ö. G. (2021). On the Framed Normal Curves in Euclidean 4-space. Fundamental Journal of Mathematics and Applications, 4(4), 258-263. https://doi.org/10.33401/fujma.992917
AMA Akyiğit M, Yıldız ÖG. On the Framed Normal Curves in Euclidean 4-space. Fundam. J. Math. Appl. Aralık 2021;4(4):258-263. doi:10.33401/fujma.992917
Chicago Akyiğit, Mahmut, ve Önder Gökmen Yıldız. “On the Framed Normal Curves in Euclidean 4-Space”. Fundamental Journal of Mathematics and Applications 4, sy. 4 (Aralık 2021): 258-63. https://doi.org/10.33401/fujma.992917.
EndNote Akyiğit M, Yıldız ÖG (01 Aralık 2021) On the Framed Normal Curves in Euclidean 4-space. Fundamental Journal of Mathematics and Applications 4 4 258–263.
IEEE M. Akyiğit ve Ö. G. Yıldız, “On the Framed Normal Curves in Euclidean 4-space”, Fundam. J. Math. Appl., c. 4, sy. 4, ss. 258–263, 2021, doi: 10.33401/fujma.992917.
ISNAD Akyiğit, Mahmut - Yıldız, Önder Gökmen. “On the Framed Normal Curves in Euclidean 4-Space”. Fundamental Journal of Mathematics and Applications 4/4 (Aralık 2021), 258-263. https://doi.org/10.33401/fujma.992917.
JAMA Akyiğit M, Yıldız ÖG. On the Framed Normal Curves in Euclidean 4-space. Fundam. J. Math. Appl. 2021;4:258–263.
MLA Akyiğit, Mahmut ve Önder Gökmen Yıldız. “On the Framed Normal Curves in Euclidean 4-Space”. Fundamental Journal of Mathematics and Applications, c. 4, sy. 4, 2021, ss. 258-63, doi:10.33401/fujma.992917.
Vancouver Akyiğit M, Yıldız ÖG. On the Framed Normal Curves in Euclidean 4-space. Fundam. J. Math. Appl. 2021;4(4):258-63.

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