Research Article
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Year 2019, Volume: 12 Issue: 2, 182 - 187, 03.10.2019
https://doi.org/10.36890/iejg.628075

Abstract

References

  • [1] Gray, A., Abbena, E. and Salamon, S., Modern differential geometry of curves and surfaces with Mathematica, 3rd Edition, Chapman Hall CRC, 2006.
  • [2] O’Neill, B., Elementary Differential Geometry, Academic Press, 1966.
  • [3] Uyar Düldül, B. and Çalışkan, M., On the geodesic torsion of a tangential intersection curve of two surfaces in R3. Acta Math. Univ. Comenian. 82 (2013), 177-189.
  • [4] Ye, X. and Maekawa, T., Differential geometry of intersection curves of two surfaces. Comput. Aided Geom. Design 16 (1999), 767-788.

Shape Operator via Darboux Frame Curvatures and Its Applications

Year 2019, Volume: 12 Issue: 2, 182 - 187, 03.10.2019
https://doi.org/10.36890/iejg.628075

Abstract

We present the shape operator’s matrix of a surface along a surface curve. By using the obtained
matrix, we give a short proof of the Beltrami-Enneper theorem. Also, we give a new method for 
determining the well-known geodesic curves of a plane, a sphere and a circular cylinder by using 
the relation between the ordinary curvatures of the geodesic and the curvatures of the surface.

References

  • [1] Gray, A., Abbena, E. and Salamon, S., Modern differential geometry of curves and surfaces with Mathematica, 3rd Edition, Chapman Hall CRC, 2006.
  • [2] O’Neill, B., Elementary Differential Geometry, Academic Press, 1966.
  • [3] Uyar Düldül, B. and Çalışkan, M., On the geodesic torsion of a tangential intersection curve of two surfaces in R3. Acta Math. Univ. Comenian. 82 (2013), 177-189.
  • [4] Ye, X. and Maekawa, T., Differential geometry of intersection curves of two surfaces. Comput. Aided Geom. Design 16 (1999), 767-788.
There are 4 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bahar Uyar Düldül

Mustfa Düldül

Publication Date October 3, 2019
Published in Issue Year 2019 Volume: 12 Issue: 2

Cite

APA Düldül, B. U., & Düldül, M. (2019). Shape Operator via Darboux Frame Curvatures and Its Applications. International Electronic Journal of Geometry, 12(2), 182-187. https://doi.org/10.36890/iejg.628075
AMA Düldül BU, Düldül M. Shape Operator via Darboux Frame Curvatures and Its Applications. Int. Electron. J. Geom. October 2019;12(2):182-187. doi:10.36890/iejg.628075
Chicago Düldül, Bahar Uyar, and Mustfa Düldül. “Shape Operator via Darboux Frame Curvatures and Its Applications”. International Electronic Journal of Geometry 12, no. 2 (October 2019): 182-87. https://doi.org/10.36890/iejg.628075.
EndNote Düldül BU, Düldül M (October 1, 2019) Shape Operator via Darboux Frame Curvatures and Its Applications. International Electronic Journal of Geometry 12 2 182–187.
IEEE B. U. Düldül and M. Düldül, “Shape Operator via Darboux Frame Curvatures and Its Applications”, Int. Electron. J. Geom., vol. 12, no. 2, pp. 182–187, 2019, doi: 10.36890/iejg.628075.
ISNAD Düldül, Bahar Uyar - Düldül, Mustfa. “Shape Operator via Darboux Frame Curvatures and Its Applications”. International Electronic Journal of Geometry 12/2 (October 2019), 182-187. https://doi.org/10.36890/iejg.628075.
JAMA Düldül BU, Düldül M. Shape Operator via Darboux Frame Curvatures and Its Applications. Int. Electron. J. Geom. 2019;12:182–187.
MLA Düldül, Bahar Uyar and Mustfa Düldül. “Shape Operator via Darboux Frame Curvatures and Its Applications”. International Electronic Journal of Geometry, vol. 12, no. 2, 2019, pp. 182-7, doi:10.36890/iejg.628075.
Vancouver Düldül BU, Düldül M. Shape Operator via Darboux Frame Curvatures and Its Applications. Int. Electron. J. Geom. 2019;12(2):182-7.