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Lie Grupta Bir Eğri Boyunca Sabit Ortalama Eğrilikli Yüzeyler Üzerine

Yıl 2023, Cilt: 13 Sayı: 2, 1230 - 1236, 01.06.2023

Zuhal Kucukarslan Yuzbasi Sevinç Taze

https://doi.org/10.21597/jist.1203363

Öz

Bu çalışmada, bir izoparametrik eğri ve onun Frenet çatısı, 3 boyutlu Lie grubunda bir yüzey oluşturmak üzere lineer olarak birleştirilmiştir. Yüzey, verilen eğri boyunca sabit bir ortalama eğriliğe sahip olduğunda, yeterli koşullar karşılanmıştır. Sonuç olarak, elde ettiklerimiz için örnekler verilmiş ve grafikler çizilmiştir.

Anahtar Kelimeler

Lie Group Mean curvature Surface.

Kaynakça

  • Bayram, E. (2022). Construction of surfaces with constant mean curvature along a timelike curve. Politeknik J., 25(3), 1211-1215.
  • Cosanoglu, H., & Bayram E. (2020). Construction of Surfaces with Constant Mean Curvature along a Curve in E’3. J. Natur. Appl. Sci., 24(3).
  • Çiftçi, Ü. (2009). A generalization of Lancret’s theorem, J. Geom. Phys. 59(12), 1597-1603.
  • Ergün, E. Bayram, E., & Kasap, E. (2014). Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sin., English Series, 30(12), 2103-2118.
  • Kasap, E., & Akyildiz F. T. (2006). Surfaces with a common geodesic in Minkowski 3-space, Appl. Math. Comp. 177, 260–270.
  • Li, C. Y. Wang, R. H., & Zhu, C. G. (2011). Parametric representation of a surface pencil with a common line of curvature. Comput. Aided Des., 43(9), 1110-1117.
  • Okuyucu, O. Z. Gök, I. Yaylı, Y., & Ekmekci, N. (2013). Slant helices in three dimensional Lie groups, Appl. Math. Comput. 221, 672-683.
  • Wang, G. J. Tang, K., & Tai, C. L. 2004. Parametric representation of a surface pencil with a common spatial geodesic, Comput. Aided Des. 36, 447–459.
  • Yoon, D. W., & Yüzbaşı Z. K. (2019). On constructions of surfaces using a geodesic in Lie group. J. Geo., 110(2), 1-10.
  • Yoon, D. W. Yüzbaşı, Z. K., & Bektaş, M. 2017. An approach for surfaces using an asymptotic curve in Lie group. J. Advan. Phys., 6(4):586-590.
  • Yoon, D. W. (2012). General helices of AW (k)-type in the Lie group, J. Appl. Math., Article ID 535123, 10 pages.

On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group

Yıl 2023, Cilt: 13 Sayı: 2, 1230 - 1236, 01.06.2023

Zuhal Kucukarslan Yuzbasi Sevinç Taze

https://doi.org/10.21597/jist.1203363

Öz

In this study, an isoparametric curve and its Frenet frame are linearly combined to form a surface in 3-dimensional Lie group. When the surface has a constant mean curvature along the given curve, sufficient conditions have been satisfied. In conclusion, we provide examples of our findings and draw graphs.

Anahtar Kelimeler

Lie Group Mean curvature Surface.

Kaynakça

  • Bayram, E. (2022). Construction of surfaces with constant mean curvature along a timelike curve. Politeknik J., 25(3), 1211-1215.
  • Cosanoglu, H., & Bayram E. (2020). Construction of Surfaces with Constant Mean Curvature along a Curve in E’3. J. Natur. Appl. Sci., 24(3).
  • Çiftçi, Ü. (2009). A generalization of Lancret’s theorem, J. Geom. Phys. 59(12), 1597-1603.
  • Ergün, E. Bayram, E., & Kasap, E. (2014). Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sin., English Series, 30(12), 2103-2118.
  • Kasap, E., & Akyildiz F. T. (2006). Surfaces with a common geodesic in Minkowski 3-space, Appl. Math. Comp. 177, 260–270.
  • Li, C. Y. Wang, R. H., & Zhu, C. G. (2011). Parametric representation of a surface pencil with a common line of curvature. Comput. Aided Des., 43(9), 1110-1117.
  • Okuyucu, O. Z. Gök, I. Yaylı, Y., & Ekmekci, N. (2013). Slant helices in three dimensional Lie groups, Appl. Math. Comput. 221, 672-683.
  • Wang, G. J. Tang, K., & Tai, C. L. 2004. Parametric representation of a surface pencil with a common spatial geodesic, Comput. Aided Des. 36, 447–459.
  • Yoon, D. W., & Yüzbaşı Z. K. (2019). On constructions of surfaces using a geodesic in Lie group. J. Geo., 110(2), 1-10.
  • Yoon, D. W. Yüzbaşı, Z. K., & Bektaş, M. 2017. An approach for surfaces using an asymptotic curve in Lie group. J. Advan. Phys., 6(4):586-590.
  • Yoon, D. W. (2012). General helices of AW (k)-type in the Lie group, J. Appl. Math., Article ID 535123, 10 pages.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Zuhal Kucukarslan Yuzbasi 0000-0001-7630-5490

Sevinç Taze 0000-0001-6892-1760

Erken Görünüm Tarihi 27 Mayıs 2023
Yayımlanma Tarihi 1 Haziran 2023
Gönderilme Tarihi 12 Kasım 2022
Kabul Tarihi 6 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 13 Sayı: 2

Kaynak Göster

APA Kucukarslan Yuzbasi, Z., & Taze, S. (2023). On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group. Journal of the Institute of Science and Technology, 13(2), 1230-1236. https://doi.org/10.21597/jist.1203363
AMA Kucukarslan Yuzbasi Z, Taze S. On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group. Iğdır Üniv. Fen Bil Enst. Der. Haziran 2023;13(2):1230-1236. doi:10.21597/jist.1203363
Chicago Kucukarslan Yuzbasi, Zuhal, ve Sevinç Taze. “On the Surfaces With Constant Mean Curvature Along a Curve in the Lie Group”. Journal of the Institute of Science and Technology 13, sy. 2 (Haziran 2023): 1230-36. https://doi.org/10.21597/jist.1203363.
EndNote Kucukarslan Yuzbasi Z, Taze S (01 Haziran 2023) On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group. Journal of the Institute of Science and Technology 13 2 1230–1236.
IEEE Z. Kucukarslan Yuzbasi ve S. Taze, “On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group”, Iğdır Üniv. Fen Bil Enst. Der., c. 13, sy. 2, ss. 1230–1236, 2023, doi: 10.21597/jist.1203363.
ISNAD Kucukarslan Yuzbasi, Zuhal - Taze, Sevinç. “On the Surfaces With Constant Mean Curvature Along a Curve in the Lie Group”. Journal of the Institute of Science and Technology 13/2 (Haziran 2023), 1230-1236. https://doi.org/10.21597/jist.1203363.
JAMA Kucukarslan Yuzbasi Z, Taze S. On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group. Iğdır Üniv. Fen Bil Enst. Der. 2023;13:1230–1236.
MLA Kucukarslan Yuzbasi, Zuhal ve Sevinç Taze. “On the Surfaces With Constant Mean Curvature Along a Curve in the Lie Group”. Journal of the Institute of Science and Technology, c. 13, sy. 2, 2023, ss. 1230-6, doi:10.21597/jist.1203363.
Vancouver Kucukarslan Yuzbasi Z, Taze S. On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group. Iğdır Üniv. Fen Bil Enst. Der. 2023;13(2):1230-6.
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