Elementary Approachs on De Sitter Space

Year 2019, , 183 - 190, 15.10.2019

Emre Öztürk , Yusuf Yaylı

https://doi.org/10.36753/mathenot.583477

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 S11(r) × R .

Keywords

De Sitter space, geodesic, curve with constant curvature

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