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A reconstruction theorem in terms of the topology and geometrical structureson the spaces of light rays and skies of a given space-time is discussed. Thisresult can be seen as part of Penrose and Low's programme intending to describethe causal structure of a space-time $M$ in terms of the topological andgeometrical properties of the space of light rays, i.e., unparametrizedtime-oriented null geodesics, $\mathcal{N}$. In the analysis of thereconstruction problem it becomes instrumental the structure of the space ofskies, i.e., of congruences of light rays. It will be shown that the space ofskies $\Sigma$ of a strongly causal skies distinguishing space-time $M$ carriesa canonical differentiable structure diffeomorphic to the original manifold$M$. Celestial curves, this is, curves in $\mathcal{N}$ which are everywheretangent to skies, play a fundamental role in the analysis of the geometry ofthe space of light rays. It will be shown that a celestial curve is induced bya past causal curve of events iff the legendrian isotopy defined by it isnon-negative. This result extends in a nontrivial way some recent results byChernov \emph{et al} on Low's Legendrian conjecture. Finally, it will be shownthat a celestial causal map between the space of light rays of two stronglycausal spaces (provided that the target space is null non-conjugate) isnecessarily induced from a conformal immersion and conversely. These resultsmake explicit the fundamental role played by the collection of skies, acollection of legendrian spheres with respect to the canonical contactstructure on $\mathcal{N}$, in characterizing the causal structure ofspace-times.

On the space of light rays of a space-time and a reconstruction theorem by Low