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M. P. Do Carmo, “Differential Geometry of Curves and Surfaces,” Prentice-Hall, Englewood Cliffs, 1976, 503 p.

has been cited by the following article:

• 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.