Special Ruled Surface in de-Sitter 3-Space

Year 2021, , 195 - 209, 30.09.2021

Tuğba Mert , Mehmet Atçeken

https://doi.org/10.33401/fujma.933725

Cited By: 2

Abstract

In this paper, timelike base curve and spacelike main geodesic with the timelike ruled surface are studied, which is a special class of ruled surface in de-Sitter space $S_{1}^{3}.$ A ruled surface in the de-Sitter space $S_{1}^{3}$ is obtained by moving a geodesic along a curve. So we will call these surfaces in the de-Sitter space as the geodesic ruled surface. Developable ruled surface, striction point, striction curve, dispersion parameter, and orthogonal trajectory concepts are investigated for the obtained geodesic ruled surface.

Keywords

Straight Geodesic, Base curve, Central Point, Central Curve

References

• [1] A. Turgut, H. Hacısaliho˘glu, Timelike ruled surface in the Minkowski-3 space, Far East J. Math. Sci., 5(1) (1997), 83-90.
• [2] A. Turgut, Spacelike and Timelike Ruled Surface on the Minkowski 3-Space, Ph. D. Thesis, Ankara University, 1995.
• [3] A. Sabuncuo˘glu, Generalized Ruled Surface, Associate Professorship Thesis, Ankara University, 1982.
• [4] T. Mert, Spacelike Ruled Surfaces in Hyperbolic 3􀀀Space, Cumhuriyet Sci. J., 39(2) (2018), 314-324.
• [5] J. Ratcliffe, Foundations of Hyperbolic Manifolds, New York, USA, 2006.
• [6] B. O’Neill, Semi-Riemannıan Geometry with applıcations to relativity, Academic Press, New York, 1983.
• [7] M. Kasedou, Spacelike submanifolds in de Sitter space, Demonstratio Mathematica, XLIII (2010), 401-418.
• [8] T. Mert, B. Karlı˘ga, Constant Angle Surface in Hyperbolic and de-Sitter 3-Spaces, Ph. D. Thesis, Gazi University, 2014.
• [9] C. Thas, A gauss map on hypersurfaces of submanıfolds ın Euclıdean spaces, J.Korean Math.Soc., 16(1) (1979), 17-27.
• [10] B. Karlı˘ga, On The Generalized Stereographic Projection, Beitr Algebra Geom., 37(2) (1996), 329-336.