@article{article_583477, title={Elementary Approachs on De Sitter Space}, journal={Mathematical Sciences and Applications E-Notes}, volume={7}, pages={183–190}, year={2019}, DOI={10.36753/mathenot.583477}, author={Öztürk, Emre and Yaylı, Yusuf}, keywords={De Sitter space,geodesic,curve with constant curvature}, abstract={<div>In this paper, we characterize the de Sitter space by means of spacelike and timelike curves that fully </div> <div>lies on it. For this purpose, we consider the tangential part of the second derivative of the unit speed </div> <div>curve on the hypersurface, and obtain the vector equations of the geodesics. We find the geodesics as </div> <div>hyperbolas, ellipses, and helices. Moreover, we give an example of null curve with constant curvature in </div> <div>4−dimensional Minkowski space and we illustrate the geodesics of S <span style="font-size:.9em;">1 </span> <span style="font-size:.9em;">1 </span> <span style="font-size:.9em;">(r) × R . </span> </div>}, number={2}, publisher={Murat TOSUN}