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

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

Abstract

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.

References

  • [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

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

Abstract

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.

References

  • [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.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Zuhal Kucukarslan Yuzbasi 0000-0001-7630-5490

Gamze Köse Şahin 0000-0003-3170-1304

Publication Date December 30, 2022
Submission Date June 25, 2022
Published in Issue Year 2022

Cite

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. December 2022;6(2):272-275. doi:10.46460/ijiea.1135754
Chicago Kucukarslan Yuzbasi, Zuhal, and Gamze Köse Şahin. “Notes on Surfaces With Constant Gauss Curvature Along a Curve in the Lie Group”. International Journal of Innovative Engineering Applications 6, no. 2 (December 2022): 272-75. https://doi.org/10.46460/ijiea.1135754.
EndNote Kucukarslan Yuzbasi Z, Köse Şahin G (December 1, 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 and G. Köse Şahin, “Notes on Surfaces with Constant Gauss Curvature along a Curve in the Lie Group”, ijiea, IJIEA, vol. 6, no. 2, pp. 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 (December 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 and Gamze Köse Şahin. “Notes on Surfaces With Constant Gauss Curvature Along a Curve in the Lie Group”. International Journal of Innovative Engineering Applications, vol. 6, no. 2, 2022, pp. 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.