Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, , 325 - 339, 27.03.2022
https://doi.org/10.18185/erzifbed.960608

Öz

Kaynakça

  • Ali, A.T. 2012. New special curves and their spherical indicatrix. Global Journal of Advanced Research On Classical and Modern Geometries, 1(2), 28-38.
  • Bishop, R.L. 1975. There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), 246-251.
  • Choi, F.H. and Kim, Y.H. 2012. Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation, 218, 9116-9124.
  • Dede, M. 2019. A new representation of tubular surfaces, Houston Journal of Mathematics, 45(3), 707-720.
  • Do Carmo, M.P. (1976). Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ.
  • Gray, A., Abbena, E. and Salamon, S. (2006). Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd Edition, Chapman and Hall/CRC, New York.
  • Izumiya, S. and Takeuchi, N. 2004. New special curves and developable surfaces. Turkish Journal of Mathematics, 28, 153-163.
  • Kızıltuğ, S. and Önder, M. 2015. Associated curves of Frenet curves in three dimensional compact Lie group. Miskolc Mathematical Notes, 16(2), 953-964.
  • Körpınar, T., Sarıaydın, M.T. and Turhan, E. 2013. Associated curves according to Bishop frame in Euclidean 3-space. Advanced Modeling and Optimization, 15(3), 713-717.
  • Kula, L. and Yaylı, Y. 2005. On slant helix and its spherical indicatrix. Applied Mathematics and Computation, 169(1), 600-607.
  • Macit, N. and Düldül, M. 2014. Some new associated curves of a Frenet curve in E3 and E4 . Turkish Journal of Mathematics, 38, 1023-1037.
  • Qian, J. and Kim, Y.H. 2015. Directional associated curves of a null curve in Minkowski 3-space. Bulletin of the Korean Mathematical Society, 52(1), 183-200.
  • Struik, D.J. (1988). Lectures On Classical Differential Geometry, Dover, New York.
  • Şahiner, B. 2019. Direction curves of tangent indicatrix of a curve. Applied Mathematics and Computation, 343, 273-284.
  • Şahiner, B. 2018. Direction curves of principal normal indicatrix of a curve. Journal of Technical Sciences, 8(2), 46-54.
  • Uzunoğlu B., Gök, İ. and Yaylı, Y. 2016. A new approach on curves of constant precession. Applied Mathematics and Computation, 275, 317-323.

Direction Curves of Spherical Indicatrices of A New Framed Curve

Yıl 2022, , 325 - 339, 27.03.2022
https://doi.org/10.18185/erzifbed.960608

Öz

In this study, direction curves of spherical indicatrix curves (primarily tangent indicatrix) for a curve in three dimensional Euclidean space were investigated. Mentioned curve was given with a new alternative frame which is {N,C,W} frame. It is a new aspect that researching relations between direction curves and the main curve via that new alternative frame. The harmonic curvatures and geodesic curvatures of spherical image of principal normal indicatrix of direction curves were obtained. The general helix, slant helix and C-slant helix characterizations of direction curves were given. Finally these curves with their figures were exemplified.

Kaynakça

  • Ali, A.T. 2012. New special curves and their spherical indicatrix. Global Journal of Advanced Research On Classical and Modern Geometries, 1(2), 28-38.
  • Bishop, R.L. 1975. There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), 246-251.
  • Choi, F.H. and Kim, Y.H. 2012. Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation, 218, 9116-9124.
  • Dede, M. 2019. A new representation of tubular surfaces, Houston Journal of Mathematics, 45(3), 707-720.
  • Do Carmo, M.P. (1976). Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs, NJ.
  • Gray, A., Abbena, E. and Salamon, S. (2006). Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd Edition, Chapman and Hall/CRC, New York.
  • Izumiya, S. and Takeuchi, N. 2004. New special curves and developable surfaces. Turkish Journal of Mathematics, 28, 153-163.
  • Kızıltuğ, S. and Önder, M. 2015. Associated curves of Frenet curves in three dimensional compact Lie group. Miskolc Mathematical Notes, 16(2), 953-964.
  • Körpınar, T., Sarıaydın, M.T. and Turhan, E. 2013. Associated curves according to Bishop frame in Euclidean 3-space. Advanced Modeling and Optimization, 15(3), 713-717.
  • Kula, L. and Yaylı, Y. 2005. On slant helix and its spherical indicatrix. Applied Mathematics and Computation, 169(1), 600-607.
  • Macit, N. and Düldül, M. 2014. Some new associated curves of a Frenet curve in E3 and E4 . Turkish Journal of Mathematics, 38, 1023-1037.
  • Qian, J. and Kim, Y.H. 2015. Directional associated curves of a null curve in Minkowski 3-space. Bulletin of the Korean Mathematical Society, 52(1), 183-200.
  • Struik, D.J. (1988). Lectures On Classical Differential Geometry, Dover, New York.
  • Şahiner, B. 2019. Direction curves of tangent indicatrix of a curve. Applied Mathematics and Computation, 343, 273-284.
  • Şahiner, B. 2018. Direction curves of principal normal indicatrix of a curve. Journal of Technical Sciences, 8(2), 46-54.
  • Uzunoğlu B., Gök, İ. and Yaylı, Y. 2016. A new approach on curves of constant precession. Applied Mathematics and Computation, 275, 317-323.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

İlkay Güven 0000-0002-5302-6074

Fatma Çolak Bu kişi benim 0000-0003-4919-4793

Yayımlanma Tarihi 27 Mart 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Güven, İ., & Çolak, F. (2022). Direction Curves of Spherical Indicatrices of A New Framed Curve. Erzincan University Journal of Science and Technology, 15(1), 325-339. https://doi.org/10.18185/erzifbed.960608