TITLE:
Some Results on the Differential Geometry of Spacelike Curves in De-Sitter Space
AUTHORS:
Tunahan Turhan, Nihat Ayyildiz
KEYWORDS:
De-Sitter Space; Frenet Equations; Frenet Reference Frame; Geodesic Curvature and Torsion; Local Canonical Form
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.3,
September
24,
2013
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.