Elementary Approachs on De Sitter Space

Abstract

In this paper, we characterize the de Sitter space by means of spacelike and timelike curves that fully lies on it. For this purpose, we consider the tangential part of the second derivative of the unit speed curve on the hypersurface, and obtain the vector equations of the geodesics. We find the geodesics as hyperbolas, ellipses, and helices. Moreover, we give an example of null curve with constant curvature in 4−dimensional Minkowski space and we illustrate the geodesics of S 1 1 (r) × R .