  We study the conformally invariant variational problem for time-like curves
in the $n$-dimensional Einstein universe defined by the conformal strain
functional. We prove that the stationary curves are trapped into an Einsetin
universe of dimension $2$, $3$ or $4$. We study the linearly-full stationary
curves in a four-dimensional Einstein universe and we show that they can be
integrated by quadratures in terms of elliptic functions, elliptic integrals
and Jacobi's theta functions.
