Lie Grupta Bir Eğri Boyunca Sabit Ortalama Eğrilikli Yüzeyler Üzerine

Year 2023, Volume: 13 Issue: 2, 1230 - 1236, 01.06.2023

Zuhal Kucukarslan Yuzbasi , Sevinç Taze

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

Abstract

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.

Keywords

Lie Group, Mean curvature, Surface.

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

Abstract

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.

Keywords

Lie Group, Mean curvature, Surface.

References

• 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.