Araştırma Makalesi
Yıl 2022,
Sayı: 40, 82 - 89, 30.09.2022
Öz
This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the TN, NB, and TB Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given TN, NB, and TB Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.
Anahtar Kelimeler
Kaynakça
- A. T. Ali, Special Smarandache Curves in the Euclidean space, International Journal of Mathematical Combinatorics 2 (2010) 30–36.
- M. Turgut, S. Yılmaz, Smarandache Curves in Minkowski Space-Time, International Journal of Mathematical Combinatorics 3 (2008) 51–55.
- C. Değirmen, O. Z. Okuyucu, Ö. G. Yıldız, Smarandache Curves in Three-Dimensional Lie Groups, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2019) 1175–1185.
- Ü. Çiftçi, A Generalization of Lancret’s Theorem, Journal of Geometry and Physics 59 (2009) 1597–1603.
- O. Z. Okuyucu, I. Gök, Y. Yaylı, N. Ekmekci, Slant Helices in Three Dimensional Lie Groups, Applied Mathematics and Computation 221 (2013) 672–683.
- D. W. Yoon, General Helices of AW(k)-Type in the Lie Group, Journal of Applied Mathematics 2012 (2012) Article ID 535123 pp. 10.
- D. W. Yoon, Z. K. Yüzbaşı, M. Bektaş, An Approach for Surfaces Using an Asymptotic Curve in Lie Group, Journal of Advanced Physics 6 (4) (2017) 586–590.
- D. W. Yoon, Z. K. Yüzbaşı, On Constructions of Surfaces Using A Geodesic in Lie Group, Journal of Geometry 110 (2) (2019) 1–10.
- G. J. Wang, K. Tang, C. L. Tai, Parametric Representation of a Surface Pencil with a Common Spatial Geodesic, Computer-Aided Design 36 (2004) 447–459.
- C. Y. Li, R. H. Wang, C. G. Zhu, Parametric Representation of a Surface Pencil with a Common Line of Curvature, Computer-Aided Design 43 (2011) 1110–1117.
- E. Kasap, F. T. Akyıldız, Surfaces with a Common Geodesic in Minkowski 3-space, Applied Mathematics and Computation 177 (2006) 260–270.
- M. Altın, A. Kazan, H. B. Karadağ, Hypersurface Families with Smarandache curves in Galilean 4-space, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 (2021) 744-761.
- E. Bayram, Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve, Journal of Polytechnic 1 (2022) pp. 7.
- H. Coşanoğlu, E. Bayram, Construction of Surfaces with Constant Mean Curvature along a Curve in E^3, Journal of Natural and Applied Sciences 24 (3) (2020) 533–538.
- E. Abbena, S. Salamon, A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition, 1998.
Yıl 2022,
Sayı: 40, 82 - 89, 30.09.2022
Öz
Kaynakça
- A. T. Ali, Special Smarandache Curves in the Euclidean space, International Journal of Mathematical Combinatorics 2 (2010) 30–36.
- M. Turgut, S. Yılmaz, Smarandache Curves in Minkowski Space-Time, International Journal of Mathematical Combinatorics 3 (2008) 51–55.
- C. Değirmen, O. Z. Okuyucu, Ö. G. Yıldız, Smarandache Curves in Three-Dimensional Lie Groups, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2019) 1175–1185.
- Ü. Çiftçi, A Generalization of Lancret’s Theorem, Journal of Geometry and Physics 59 (2009) 1597–1603.
- O. Z. Okuyucu, I. Gök, Y. Yaylı, N. Ekmekci, Slant Helices in Three Dimensional Lie Groups, Applied Mathematics and Computation 221 (2013) 672–683.
- D. W. Yoon, General Helices of AW(k)-Type in the Lie Group, Journal of Applied Mathematics 2012 (2012) Article ID 535123 pp. 10.
- D. W. Yoon, Z. K. Yüzbaşı, M. Bektaş, An Approach for Surfaces Using an Asymptotic Curve in Lie Group, Journal of Advanced Physics 6 (4) (2017) 586–590.
- D. W. Yoon, Z. K. Yüzbaşı, On Constructions of Surfaces Using A Geodesic in Lie Group, Journal of Geometry 110 (2) (2019) 1–10.
- G. J. Wang, K. Tang, C. L. Tai, Parametric Representation of a Surface Pencil with a Common Spatial Geodesic, Computer-Aided Design 36 (2004) 447–459.
- C. Y. Li, R. H. Wang, C. G. Zhu, Parametric Representation of a Surface Pencil with a Common Line of Curvature, Computer-Aided Design 43 (2011) 1110–1117.
- E. Kasap, F. T. Akyıldız, Surfaces with a Common Geodesic in Minkowski 3-space, Applied Mathematics and Computation 177 (2006) 260–270.
- M. Altın, A. Kazan, H. B. Karadağ, Hypersurface Families with Smarandache curves in Galilean 4-space, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 (2021) 744-761.
- E. Bayram, Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve, Journal of Polytechnic 1 (2022) pp. 7.
- H. Coşanoğlu, E. Bayram, Construction of Surfaces with Constant Mean Curvature along a Curve in E^3, Journal of Natural and Applied Sciences 24 (3) (2020) 533–538.
- E. Abbena, S. Salamon, A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition, 1998.
Toplam 15 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2022 |
| Gönderilme Tarihi | 23 Ağustos 2022 |
| Yayımlandığı Sayı | Yıl 2022 Sayı: 40 |
Kaynak Göster
- Makale Dosyaları
|