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

Tunahan Turhan, Nihat Ayyildiz

Department of Mathematics, Süleyman Demirel University, Isparta, Turkey.
Seydi?ehir Vocational School, Necmettin Erbakan University, Konya, Turkey.

DOI: 10.4236/jamp.2013.13009                

Abstract

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.

Keywords

De-Sitter Space; Frenet Equations; Frenet Reference Frame; Geodesic Curvature and Torsion; Local Canonical Form

Conflicts of Interest

The authors declare no conflicts of interest.

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