Timelike Ruled Surfaces in de-Sitter 3-Space

Year 2020, Volume: 12 Issue: 2, 166 - 175, 31.12.2020

Tuğba Mert

https://doi.org/10.47000/tjmcs.734243

Cited By: 1

Abstract

In this paper, timelike ruled surfaces are studied 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. Developable ruled surface, striction point, striction curve, dispersion parameter and orthogonal trajectory concepts are investigated for the obtained ruled surface.

Keywords

Straight Geodesic , Base Curve , Central Point , Central Curve

References

• Kasedou, M., Spacelike submanifolds in de sitter space, Demonstratio Mathematica, XLIII(2)(2010), 401--418.
• Mert,T., Spacelike ruled surfaces in hyperbolic 3-space, Cumhuriyet Sci. J., 39(2)(2018), 314--324.
• O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
• Ratcliffe, J., Foundations of Hyperbolic Manifolds, Springer, 1994.
• Sabuncuoğllu, A., Generelized Ruled Surface, Associate Proffesorshiph Thesis, Ankara University, 1982.
• Thas, C., A gauss map on hypersurfaces of submanifolds in Euclidean spaces, J.Korean Math. Soc., 16(1)(1979), 17--27.
• Turgut, A., Spacelike and Timelike Ruled Surface on the Minkowski 3-Space, Ph. D. Thesis, Ankara University, 1995.
• Turgut, A., Hacısalihoğlu, H., Timelike ruled surface in the Minkowski 3-space, Far East J. Math. Sci., 5(1)(1997), 83--90.