Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 2, 444 - 452, 11.04.2021
https://doi.org/10.15672/hujms.664764

Öz

Kaynakça

  • [1] W.J. Che and J.C. Paul, Lines of curvature and umbilical points for implicit surfaces, Comput. Aided Geom. Design, 24 (7), 395–409, 2007.
  • [2] Ü. Çiftçi, A generalization of Lancret’s theorem, J. Geom. Phys. 59 (12), 1597–1603, 2009.
  • [3] M.P. do Carmo, Differential Geometry of Curves and Surfaces, Englewood Cliffs: Prentice Hall, 1976.
  • [4] N. do Espírito-Santo, S. Fornari, K. Frensel and J. Ripoll, Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric, Manuscripta Math. 111 (4), 459–470, 2003.
  • [5] E. Evren, E. Bayram and E. Kasap, Surface pencil with a common line of curvature in Minkowski 3-space, Acta Math. Sin. (Engl. Ser.) 30 (12), 2103–2118, 2014.
  • [6] C.Y. Li, R.H. Wang and C.G. Zhu, Parametric representation of a surface pencil with a common line of curvature, Comput. Aided Design, 43 (9), 1110–1117, 2011.
  • [7] C.Y. Li, R.H. Wang and C.G. Zhu, An approach for designing a developable surface through a given line of curvature, Comput. Aided Design, 45, 621–627, 2013
  • [8] C.Y. Li, C.G. Zhu and R.H. Wang, A generalization of surface family with common line of curvature, Appl. Math. Comput. 219 (17), 9500–9507, 2013.
  • [9] C.Y. Li, C.G. Zhu and R.H. Wang, Spacelike developable surfaces through a common line of curvature in Minkowski space, J. Adv. Mech. Des. Syst. Manuf. 9 (4), 1–9, 2015.
  • [10] T. Maekawa, F.E. Wolter and N.M. Patrikalakis, Umbilics and lines of curvature for shape interrogation, Comput. Aided Geom. Design, 13 (2), 133–161, 1996
  • [11] T.J. Willmore, An Introduction to Differential Geometry, Oxford University Press, 1959.
  • [12] D.W. Yoon, General helices of AW(k)-type in the Lie group, J. Appl. Math. 2012, Art. No. 535123, 2012.
  • [13] X.P. Zhang, W.J. Che and J.C. Paul, Computing lines of curvature for implicit surfaces, Comput. Aided Geom. Design, 26 (9), 923–940, 2009.

A generalization for surfaces using a line of curvature in Lie group

Yıl 2021, Cilt: 50 Sayı: 2, 444 - 452, 11.04.2021
https://doi.org/10.15672/hujms.664764

Öz

In this study, we investigate how to construct surfaces using a line of curvature in a 3-dimensional Lie group. Then, by utilizing the Frenet frame, we give the conditions that a curve becomes a line of curvature on a surface when the marching-scale functions are more general expressions. After then, we provide some crucial examples of how efficient our method is on these surfaces.

Kaynakça

  • [1] W.J. Che and J.C. Paul, Lines of curvature and umbilical points for implicit surfaces, Comput. Aided Geom. Design, 24 (7), 395–409, 2007.
  • [2] Ü. Çiftçi, A generalization of Lancret’s theorem, J. Geom. Phys. 59 (12), 1597–1603, 2009.
  • [3] M.P. do Carmo, Differential Geometry of Curves and Surfaces, Englewood Cliffs: Prentice Hall, 1976.
  • [4] N. do Espírito-Santo, S. Fornari, K. Frensel and J. Ripoll, Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric, Manuscripta Math. 111 (4), 459–470, 2003.
  • [5] E. Evren, E. Bayram and E. Kasap, Surface pencil with a common line of curvature in Minkowski 3-space, Acta Math. Sin. (Engl. Ser.) 30 (12), 2103–2118, 2014.
  • [6] C.Y. Li, R.H. Wang and C.G. Zhu, Parametric representation of a surface pencil with a common line of curvature, Comput. Aided Design, 43 (9), 1110–1117, 2011.
  • [7] C.Y. Li, R.H. Wang and C.G. Zhu, An approach for designing a developable surface through a given line of curvature, Comput. Aided Design, 45, 621–627, 2013
  • [8] C.Y. Li, C.G. Zhu and R.H. Wang, A generalization of surface family with common line of curvature, Appl. Math. Comput. 219 (17), 9500–9507, 2013.
  • [9] C.Y. Li, C.G. Zhu and R.H. Wang, Spacelike developable surfaces through a common line of curvature in Minkowski space, J. Adv. Mech. Des. Syst. Manuf. 9 (4), 1–9, 2015.
  • [10] T. Maekawa, F.E. Wolter and N.M. Patrikalakis, Umbilics and lines of curvature for shape interrogation, Comput. Aided Geom. Design, 13 (2), 133–161, 1996
  • [11] T.J. Willmore, An Introduction to Differential Geometry, Oxford University Press, 1959.
  • [12] D.W. Yoon, General helices of AW(k)-type in the Lie group, J. Appl. Math. 2012, Art. No. 535123, 2012.
  • [13] X.P. Zhang, W.J. Che and J.C. Paul, Computing lines of curvature for implicit surfaces, Comput. Aided Geom. Design, 26 (9), 923–940, 2009.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Dae Won Yoon 0000-0001-8620-0676

Zuhal Kucukarslan Yuzbasi 0000-0001-7630-5490

Yayımlanma Tarihi 11 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 2

Kaynak Göster

APA Yoon, D. W., & Kucukarslan Yuzbasi, Z. (2021). A generalization for surfaces using a line of curvature in Lie group. Hacettepe Journal of Mathematics and Statistics, 50(2), 444-452. https://doi.org/10.15672/hujms.664764
AMA Yoon DW, Kucukarslan Yuzbasi Z. A generalization for surfaces using a line of curvature in Lie group. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):444-452. doi:10.15672/hujms.664764
Chicago Yoon, Dae Won, ve Zuhal Kucukarslan Yuzbasi. “A Generalization for Surfaces Using a Line of Curvature in Lie Group”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 444-52. https://doi.org/10.15672/hujms.664764.
EndNote Yoon DW, Kucukarslan Yuzbasi Z (01 Nisan 2021) A generalization for surfaces using a line of curvature in Lie group. Hacettepe Journal of Mathematics and Statistics 50 2 444–452.
IEEE D. W. Yoon ve Z. Kucukarslan Yuzbasi, “A generalization for surfaces using a line of curvature in Lie group”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 444–452, 2021, doi: 10.15672/hujms.664764.
ISNAD Yoon, Dae Won - Kucukarslan Yuzbasi, Zuhal. “A Generalization for Surfaces Using a Line of Curvature in Lie Group”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 444-452. https://doi.org/10.15672/hujms.664764.
JAMA Yoon DW, Kucukarslan Yuzbasi Z. A generalization for surfaces using a line of curvature in Lie group. Hacettepe Journal of Mathematics and Statistics. 2021;50:444–452.
MLA Yoon, Dae Won ve Zuhal Kucukarslan Yuzbasi. “A Generalization for Surfaces Using a Line of Curvature in Lie Group”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 444-52, doi:10.15672/hujms.664764.
Vancouver Yoon DW, Kucukarslan Yuzbasi Z. A generalization for surfaces using a line of curvature in Lie group. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):444-52.