Ruled Surfaces with Constant Slope Ruling According to Darboux Frame in Minkowski Space

Article Sidebar

PDF
Cite as:
AyÅŸe Yavuz, Yusuf Yayli, Ruled Surfaces with Constant Slope Ruling According to Darboux Frame in Minkowski Space, Int. J. Anal. Appl., 18 (6) (2020), 900-919.

Main Article Content

AyÅŸe Yavuz, Yusuf Yayli

Abstract

In this study, three different types of ruled surfaces are defined. The generating lines of these ruled surfaces are given by points on a curve X in Minkowski Space, while the position vector of X have constant slope with respect to the planes (t, y), (t, n), (n, y). It is observed that the Lorentzian casual characters of the ruled surfaces with constant slope can be timelike or spacelike. Furthermore, striction lines of these surfaces are obtained and investigated under various special cases. Finally, new investigations are obtained on the base curve of these types of ruled surfaces.

Article Details

References

  1. A.T. Ali, Special Smarandache Curves in the Euclidean Space. Int. J. Math. Comb. 2 (2010), 30-36.
  2. H.H. Ugurlu, H. Kocayigit, The Frenet and Darboux Instantaneous Rotain Vectors of Curves on Timelike Surfaces, Math. Comput. Appl. 1 (2) (1996), 133-141.
  3. S. Kiziltug, A. Cakmak, Developable Ruled Surfaces with Darboux Frame in Minkowski 3-Space. Life Science Journal (2013), 10(4).
  4. S. Kiziltug, Y. Yayli, Timelike Curves on Timelike Parallel Surfaces in Minkowski 3-Space E3 1 , Math. Aeterna, 2 (2012), 689 - 700.
  5. S. N. Krivoshapko, S. Shambina, Design of Developable Surfaces and The Application of Thin-Walled Developable Structures, Serbian Architect. J. 4 (3) (2012), 298-317.
  6. R. Lopez, Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. Int. Electron. J. Geom. 7 (1) (2014), 44-107.
  7. K. Malecek, J. Szarka, D. Szarkova, Surfaces with Constant Slope with Their Generalisation. J. Polish Soc. Geom. Eng. Graph. 19 (2009), 67-77.
  8. B. O'Neill, Elementary Differential Geometry, Academic Press, New York, 1966.
  9. M. Onder, H.H. Ugurlu, Frenet Frames and Invariants of Timelike Ruled Surfaces, Ain Shams Eng. J. 4 (3) (2013), 507-513.
  10. A. Yavuz, F. Ates, Y. Yayli, Non-null Surfaces with Constant Slope Ruling with Respect to Osculating Plane. Adiyaman Univ. J. Sci. 10 (2020), 240-255.