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Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group

Yıl 2022, , 272 - 275, 30.12.2022
https://doi.org/10.46460/ijiea.1135754

Öz

In this study, sufficient conditions are derived and examples are created to derive surfaces with constant Gauss curvature along a given curve in terms of the linear combination of its Frenet frame in the 3-dimensional Lie group.

Kaynakça

  • [1] 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.
  • [2] 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.
  • [3] Ergün, E., Bayram, & Kasap, E., (2014). Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sin. (Engl. Ser.), 30(12), 2103-2118.
  • [4] Kasap, E., & Akyildiz, F. T. (2006). Surfaces with a common geodesic in Minkowski 3-space., Appl. Math. Comp. , 177, 260–270.
  • [5] Yoon, D. W., Yüzbaşi, Z. K., & Bektaş, M. (2017). An approach for surfaces using an asymptotic curve in Lie group. J. Advan. Phys., 6(4), 586-590.
  • [6] Yoon, D. W., & Yüzbaşi, Z. K. (2019). On constructions of surfaces using a geodesic in Lie group, J. Geo., 110(2), 1-10.
  • [7] Bayram, E. (2022). Construction of surfaces with constant mean curvature along a timelike curve. Politeknik Dergisi, 1-1.
  • [8] Bayram, E. (2020). Verilen Bir Eğri Boyunca Gauss Eğriliği Sabit Olan Yüzeyler. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 20(5), 819-823.
  • [9] Çiftçi, Ü. (2009). A generalization of Lancret’s theorem, J. Geom. Phys., 59(12) , 1597-1603.
  • [10] Okuyucu, O. Z., Gök, İ, Yaylı Y., & Ekmekci N. (2013) Slant helices in three dimensional Lie groups, Appl. Math. Comput., 221, 672-683.
  • [11] Yoon, D.W. (2012). General helices of AW (k)-type in the Lie group, J. Appl. Math., Article ID 535123, 10 pages.
  • [12] Abbena, E., Salamon, S., & Gray, A. Modern differential geometry of curves and surfaces with mathematica. Third Edition, 1998.

Lie Grubunda Bir Eğri Boyunca Sabit Gauss Eğrilikli Yüzeyler Üzeine Notlar

Yıl 2022, , 272 - 275, 30.12.2022
https://doi.org/10.46460/ijiea.1135754

Öz

Bu çalışmada, 3-boyutlu Lie grupta verilen eğrinin Frenet çatısının lineer kombinasyonuna göre verilen bir eğri boyunca sabit Gauss eğriliğine sahip yüzeyleri bulmak için yeterli koşullar üretilmiş ve örnekler oluşturulmuştur.

Kaynakça

  • [1] 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.
  • [2] 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.
  • [3] Ergün, E., Bayram, & Kasap, E., (2014). Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sin. (Engl. Ser.), 30(12), 2103-2118.
  • [4] Kasap, E., & Akyildiz, F. T. (2006). Surfaces with a common geodesic in Minkowski 3-space., Appl. Math. Comp. , 177, 260–270.
  • [5] Yoon, D. W., Yüzbaşi, Z. K., & Bektaş, M. (2017). An approach for surfaces using an asymptotic curve in Lie group. J. Advan. Phys., 6(4), 586-590.
  • [6] Yoon, D. W., & Yüzbaşi, Z. K. (2019). On constructions of surfaces using a geodesic in Lie group, J. Geo., 110(2), 1-10.
  • [7] Bayram, E. (2022). Construction of surfaces with constant mean curvature along a timelike curve. Politeknik Dergisi, 1-1.
  • [8] Bayram, E. (2020). Verilen Bir Eğri Boyunca Gauss Eğriliği Sabit Olan Yüzeyler. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 20(5), 819-823.
  • [9] Çiftçi, Ü. (2009). A generalization of Lancret’s theorem, J. Geom. Phys., 59(12) , 1597-1603.
  • [10] Okuyucu, O. Z., Gök, İ, Yaylı Y., & Ekmekci N. (2013) Slant helices in three dimensional Lie groups, Appl. Math. Comput., 221, 672-683.
  • [11] Yoon, D.W. (2012). General helices of AW (k)-type in the Lie group, J. Appl. Math., Article ID 535123, 10 pages.
  • [12] Abbena, E., Salamon, S., & Gray, A. Modern differential geometry of curves and surfaces with mathematica. Third Edition, 1998.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Zuhal Kucukarslan Yuzbasi 0000-0001-7630-5490

Gamze Köse Şahin 0000-0003-3170-1304

Yayımlanma Tarihi 30 Aralık 2022
Gönderilme Tarihi 25 Haziran 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Kucukarslan Yuzbasi, Z., & Köse Şahin, G. (2022). Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group. International Journal of Innovative Engineering Applications, 6(2), 272-275. https://doi.org/10.46460/ijiea.1135754
AMA Kucukarslan Yuzbasi Z, Köse Şahin G. Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group. ijiea, IJIEA. Aralık 2022;6(2):272-275. doi:10.46460/ijiea.1135754
Chicago Kucukarslan Yuzbasi, Zuhal, ve Gamze Köse Şahin. “Notes on Surfaces With Constant Gauss Curvature Along a Curve in the Lie Group”. International Journal of Innovative Engineering Applications 6, sy. 2 (Aralık 2022): 272-75. https://doi.org/10.46460/ijiea.1135754.
EndNote Kucukarslan Yuzbasi Z, Köse Şahin G (01 Aralık 2022) Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group. International Journal of Innovative Engineering Applications 6 2 272–275.
IEEE Z. Kucukarslan Yuzbasi ve G. Köse Şahin, “Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group”, ijiea, IJIEA, c. 6, sy. 2, ss. 272–275, 2022, doi: 10.46460/ijiea.1135754.
ISNAD Kucukarslan Yuzbasi, Zuhal - Köse Şahin, Gamze. “Notes on Surfaces With Constant Gauss Curvature Along a Curve in the Lie Group”. International Journal of Innovative Engineering Applications 6/2 (Aralık 2022), 272-275. https://doi.org/10.46460/ijiea.1135754.
JAMA Kucukarslan Yuzbasi Z, Köse Şahin G. Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group. ijiea, IJIEA. 2022;6:272–275.
MLA Kucukarslan Yuzbasi, Zuhal ve Gamze Köse Şahin. “Notes on Surfaces With Constant Gauss Curvature Along a Curve in the Lie Group”. International Journal of Innovative Engineering Applications, c. 6, sy. 2, 2022, ss. 272-5, doi:10.46460/ijiea.1135754.
Vancouver Kucukarslan Yuzbasi Z, Köse Şahin G. Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group. ijiea, IJIEA. 2022;6(2):272-5.