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arXiv · 1605.06783

A conformally invariant variational problem for time-like curves

Olimjon Eshkobilov·Emilio Musso
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Abstract

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.

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Olimjon Eshkobilov, Emilio Musso. 2016-05-22. A conformally invariant variational problem for time-like curves. https://arxiv.org/abs/1605.06783

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