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.
References
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[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.
http://dx.doi.org/10.1007/s00022-007-1944-5
[3]
M. Kasedou, “Singularities of Lightcone Gauss Images of Spacelike Hypersurfaces in de Sitter Space,” Journal of Geometry, Vol. 94, 2009, pp. 107-121.
http://dx.doi.org/10.1007/s00022-009-0001-y
[4]
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http://dx.doi.org/10.1016/0094-114X(87)90003-6
[5]
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http://dx.doi.org/10.1115/1.3267417
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M. P. Do Carmo, “Differential Geometry of Curves and Surfaces,” Prentice-Hall, Englewood Cliffs, 1976, 503 p.
