Ruled Surfaces with Constant Slope Ruling According to Darboux Frame

Year 2020, Volume: 8 Issue: 2, 135 - 144, 15.10.2020

Ayşe Yavuz Fatma Ateş Yusuf Yaylı

https://doi.org/10.36753/mathenot.640345

Abstract

 The main scope of this paper is to examine ruled surfaces with constant slope ruling with respect to the given surface according to Darboux Frame. We give necessary and su¢ cient conditions for these types surfaces to be developable. Also, the investigations are observed under some special cases. Especially we obtained that the striction lines and Gaussian curvature of the surfaces.                                                                                                                                                                                  .

Keywords

Ruled Surface, Surface with Constant Slope, Darboux Frame

References

• [1] Do Carmo, M. P.: Differential Geometry of Curves and Surfaces. Prentice-Hall, ISBN 0-13-212589- 7 (1976).
• [2] Hacısalihoğlu H.H.: Differential Geometry. Ankara, Faculty of Science Publ. (2000).
• [3] Malecek K, Szarka J, Szarková D : Surfaces With Constant Slope and Their Generalization. J. Polish Society Geometry Eng. Graphics, 19:67-77 (2009).
• [4] Sabuncuoğlu A. : Differential Geometry, Nobel Publication. ISBN978-975-591-237-0. Ankara (2010).
• [5] Papageorgiou S. G., Aspragathos N. A.: Rational ruled surfaces construction by interpolating dual unit vectors representing lines. In: International Conference on Computer graphics, Visualization and Computer Vision, Pilzen, Czech Republic, 30 January–3 February 2006. Pilzen: WSCG, University of West Bohemia ( 2006).