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

A conformally invariant variational problem for time-like curves