Tschirnhausen Helical Surface in Three Dimensional Euclidean Space


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Authors

Keywords:

Euclidean 3-Space, Helical Surface, Tschirnhausen Helical Surface, Gauss Map, Curvature

Abstract

The main aim of this research is to reveal Tschirnhausen helical surface in three-dimensional Euclidean space E3. We construct Tschirnhausen helical surface, and obtain its Gauss map, Gaussian curvature, mean curvature. Moreover, we compute some relations of the curvatures of that kind surface.

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Author Biographies

Erhan Güler , Bartın University

Department of Mathematics, Faculty of Sciences, Turkey

Ömer Kişi, Bartın University

Department of Mathematics, Faculty of Sciences, Turkey

References

L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces. Dover Publications, N.Y. 1909.

A.R. Forsyth, Lectures on the Differential Geometry of Curves and Surfaces. Cambridge Un. press, 2nd ed. 1920.

A. Gray, S. Salamon, and E. Abbena, Modern Differential Geometry of Curves and Surfaces with Mathematica. Third ed. Chapman & Hall/CRC Press, Boca Raton, 2006.

H.H. Hacısalihoğlu, Diferensiyel Geometri I. Ankara Ün., Ankara, 1982.

H.H. Hacısalihoğlu, 2 ve 3 Boyutlu Uzaylarda Analitik Geometri. Ertem basım, Ankara, 2013.

J.C.C. Nitsche, Lectures on Minimal Surfaces, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems. Cambridge University Press, Cambridge, 1989.

M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. IV. Third edition. Publish or Perish, Inc., Houston, Texas, 1999.

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Published

2023-02-02

How to Cite

Güler , E., & Kişi, Ömer. (2023). Tschirnhausen Helical Surface in Three Dimensional Euclidean Space. International Conference on Innovative Academic Studies, 2, 19–27. Retrieved from https://as-proceeding.com/index.php/icias/article/view/10

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Conference Papers