  Our recent results concerning the transformation under isometries of the
conserved quantities on de Sitter manifolds, allow us to define the rest frame
and study the relative geodesic motion in terms of conserved momentum,
revealing thus various relativistic effects [I. I. Cotaescu, arXiv:1701.08499].
Here we discuss the time dilation (of the twin paradox) and the Lorentz
contraction on the de Sitter expanding portions, pointing out the dependence of
these effects on the position and moment in which the time and lengths are
measured.
