Some Results on the Differential Geometry of Spacelike Curves in De-Sitter Space


The differential geometry of curves on a hypersphere in the Euclidean space reflects instantaneous properties of spherecal motion. In this work, we give some results for differential geometry of spacelike curves in 3-dimensional de-Sitter space. Also, we study the Frenet reference frame, the Frenet equations, and the geodesic curvature and torsion functions to analyze and characterize the shape of the curves in 3-dimensional de-Sitter space.

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Turhan, T. and Ayyildiz, N. (2013) Some Results on the Differential Geometry of Spacelike Curves in De-Sitter Space. Journal of Applied Mathematics and Physics, 1, 55-59. doi: 10.4236/jamp.2013.13009.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] B. O’Neill, “Semi-Riemann Geometry: With Applictions to Relativity,” Academic Press, New York, 1983, 469 p.
[2] T. Fusho and S. Izumiya, “Lightlike Surfaces of Spacelike Curves in de Sitter 3-Space,” Journal of Geometry, Vol. 88, 2008, pp. 19-29.
[3] M. Kasedou, “Singularities of Lightcone Gauss Images of Spacelike Hypersurfaces in de Sitter Space,” Journal of Geometry, Vol. 94, 2009, pp. 107-121.
[4] J. M. McCarthy, “The Differential Geometry of Curves in an Image Space of Spherical Kinematics,” Mechanism and Machine Theory, Vol. 22, No. 3, 1987, pp. 205-211.
[5] J. M. McCarthy and B. Ravani, “Differential Kinematics of Spherical and Spatial Motions Using Kinematic Mapping,” Journal of Applied Mechanics, Vol. 53, No. 1, 1986, pp. 15-22.
[6] B. Ravani and B. Roth, “Mappings of Spatial Kinematics,” Journal of Mechanisms, Transmissions and Automation in Design, Vol. 106, No. 3, 1984, pp. 341-347.
[7] M. P. Do Carmo, “Differential Geometry of Curves and Surfaces,” Prentice-Hall, Englewood Cliffs, 1976, 503 p.

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