Araştırma Makalesi
BibTex RIS Kaynak Göster

Characterizations of Inclined Curves According to Parallel Transport Frame in E 4 and Bishop Frame in E 3

Yıl 2019, Cilt: 7 Sayı: 1, 16 - 24, 15.04.2019

Öz

Kaynakça

  • [1] M. Barros, General helices and a theorem of Lancert. Proc. AMS (1997), 125, 1503-9.
  • [2] L.R. Bishop, There is more than one way to frame a curve. Amer. Math. Monthly, Volume 82, Issue 3, (1975) 246-251.
  • [3] B. Bükcü, M. K. Karacan, The Slant Helices According to Bishop Frame, International Journal of Computational and Mathematical Sciences 3:2 (2009).
  • [4] Ç . Camcı, K. İIlarslan, L. Kula, H. H. Hacısalihoğlu, Harmonic curvatures and generalized helices in En; Chaos, Solitons and Fractals, 40 (2007), 1-7.
  • [5] E. Özdamar, H. H. Hacısalihoğlu, A characterization of inclined curves in Euclidean n-space, Communication de la faculte´ des sciences de L’Universite´ d’Ankara, s´eries A1, 24A (1975),15-22.
  • [6] G. Harary, A. Tal, 3D Euler Spirals for 3D Curve Completion, Symposium on Computational Geometry 2010: 107-108.
  • [7] F. Gökçelik , Z. Bozkurt, İ. Gök, F. N. Ekmekci, Y. Yaylı, Parallel transport frame in 4-dimensional Euclidean space E4; Caspian Journal of Mathematical Sciences (CJMS), Vol. 3 (1), (2014), 103-113.
  • [8] A. J. Hanson and H. Ma, Parallel Transport Aproach to curve Framing, Tech. Math. Rep. 425(1995), Indiana University Computer science Department.
  • [9] İ. Gök, C. Camci, H. H. Hacisalihoğlu, Vn􀀀slant helices in Euclideann n-space En; Mathematical communications 317 Math. Commun., 14(2009), No. 2, 317-329.
  • [10] L. Kula, Y.Yayli, On slant helix and its spherical indicatrix, Appl. Math. and Comp. 169(2005), 600–607.
  • [11] T. Korpinar, E. Turhan and V. Asil, Tangent Bishop spherical images of a biharmonic B-slant helix in the Heisenberg group Heis3; Iranian Journal of Science & Technology, IJST (2011) A4: 265-271.
  • [12] J. Monterde, Curves with constant curvature ratios, Boletin de la Sociedad Matematica Mexicana13(2007), 177–186.
  • [13] A. B. Samuel J. Jasper, Helices in a flat space of four dimensions, Master Thesis, The Ohio State University (1946).
  • [14] S. Yılmaz, E. O¨ zyılmaz, M. Turgut, New Spherical Indicatrices and Their Characterizations, An. S¸ t. Univ. Ovidius Constan¸ta, Vol. 18 (2), (2010) 337-354.

Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$

Yıl 2019, Cilt: 7 Sayı: 1, 16 - 24, 15.04.2019

Öz

The aim of this paper is to introduce inclined curves according to parallel transport frame. This paper begins by defined a vector field D called Darboux vector field of an inclined curve in E 4
. It will then go on to an alternative characterization for the inclined curves “α : I ⊂ R −→ E 4 is an inclined curve ⇔ k1(s) Z k1(s)ds+k2(s) Z k2(s)ds+k3(s) Z k3(s)ds = 0” where k1(s), k2(s), k3(s) are the principal curvature functions according to parallel transport frame of the curve α and also, similar characterization for the generalized helices according to Bishop frame in E
3 is given by α : I ⊂ R −→ E 3 is a generalized helix ⇔ k1(s) Z k1(s)ds+k2(s) Z k2(s)ds = 0” where k1(s), k2(s) are the principal curvature functions according to Bishop frame of the curve α. These curves have illustrated some examples and draw their figures with use of Mathematica programming language. Also, it is given an example for the inclined curve in E 4 and showed that the above condition is satisfied for this curve.

Kaynakça

  • [1] M. Barros, General helices and a theorem of Lancert. Proc. AMS (1997), 125, 1503-9.
  • [2] L.R. Bishop, There is more than one way to frame a curve. Amer. Math. Monthly, Volume 82, Issue 3, (1975) 246-251.
  • [3] B. Bükcü, M. K. Karacan, The Slant Helices According to Bishop Frame, International Journal of Computational and Mathematical Sciences 3:2 (2009).
  • [4] Ç . Camcı, K. İIlarslan, L. Kula, H. H. Hacısalihoğlu, Harmonic curvatures and generalized helices in En; Chaos, Solitons and Fractals, 40 (2007), 1-7.
  • [5] E. Özdamar, H. H. Hacısalihoğlu, A characterization of inclined curves in Euclidean n-space, Communication de la faculte´ des sciences de L’Universite´ d’Ankara, s´eries A1, 24A (1975),15-22.
  • [6] G. Harary, A. Tal, 3D Euler Spirals for 3D Curve Completion, Symposium on Computational Geometry 2010: 107-108.
  • [7] F. Gökçelik , Z. Bozkurt, İ. Gök, F. N. Ekmekci, Y. Yaylı, Parallel transport frame in 4-dimensional Euclidean space E4; Caspian Journal of Mathematical Sciences (CJMS), Vol. 3 (1), (2014), 103-113.
  • [8] A. J. Hanson and H. Ma, Parallel Transport Aproach to curve Framing, Tech. Math. Rep. 425(1995), Indiana University Computer science Department.
  • [9] İ. Gök, C. Camci, H. H. Hacisalihoğlu, Vn􀀀slant helices in Euclideann n-space En; Mathematical communications 317 Math. Commun., 14(2009), No. 2, 317-329.
  • [10] L. Kula, Y.Yayli, On slant helix and its spherical indicatrix, Appl. Math. and Comp. 169(2005), 600–607.
  • [11] T. Korpinar, E. Turhan and V. Asil, Tangent Bishop spherical images of a biharmonic B-slant helix in the Heisenberg group Heis3; Iranian Journal of Science & Technology, IJST (2011) A4: 265-271.
  • [12] J. Monterde, Curves with constant curvature ratios, Boletin de la Sociedad Matematica Mexicana13(2007), 177–186.
  • [13] A. B. Samuel J. Jasper, Helices in a flat space of four dimensions, Master Thesis, The Ohio State University (1946).
  • [14] S. Yılmaz, E. O¨ zyılmaz, M. Turgut, New Spherical Indicatrices and Their Characterizations, An. S¸ t. Univ. Ovidius Constan¸ta, Vol. 18 (2), (2010) 337-354.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Fatma Ateş 0000-0002-3529-1077

İsmail Gok

Faik Nejat Ekmekci

Yusuf Yaylı

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 12 Şubat 2019
Kabul Tarihi 21 Şubat 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

APA Ateş, F., Gok, İ., Ekmekci, F. N., Yaylı, Y. (2019). Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp Journal of Mathematics, 7(1), 16-24.
AMA Ateş F, Gok İ, Ekmekci FN, Yaylı Y. Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp J. Math. Nisan 2019;7(1):16-24.
Chicago Ateş, Fatma, İsmail Gok, Faik Nejat Ekmekci, ve Yusuf Yaylı. “Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 16-24.
EndNote Ateş F, Gok İ, Ekmekci FN, Yaylı Y (01 Nisan 2019) Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp Journal of Mathematics 7 1 16–24.
IEEE F. Ateş, İ. Gok, F. N. Ekmekci, ve Y. Yaylı, “Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$”, Konuralp J. Math., c. 7, sy. 1, ss. 16–24, 2019.
ISNAD Ateş, Fatma vd. “Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$”. Konuralp Journal of Mathematics 7/1 (Nisan 2019), 16-24.
JAMA Ateş F, Gok İ, Ekmekci FN, Yaylı Y. Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp J. Math. 2019;7:16–24.
MLA Ateş, Fatma vd. “Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 16-24.
Vancouver Ateş F, Gok İ, Ekmekci FN, Yaylı Y. Characterizations of Inclined Curves According to Parallel Transport Frame in $E^{4}$ and Bishop Frame in $E^{3}$. Konuralp J. Math. 2019;7(1):16-24.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.