We present the state-of-the-art concerning the relativistic constraints, which describe the geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review a variety of solvability results, the construction of several classes of solutions of special relevance and place results in the broader context of mathematical general relativity. Apart from providing an overview of the subject, this paper includes a selection of open questions, as well as a few complements to some significant contributions in the literature.

中文翻译：

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广义相对论约束方程

我们提出了有关相对论约束的最新技术，它描述了受爱因斯坦场方程约束的时空中超曲面的几何形状。我们回顾了各种可解性结果，构建了几类具有特殊相关性的解决方案，并将结果置于更广泛的数学广义相对论背景中。除了提供该主题的概述之外，本文还包括一些开放问题的选择，以及对文献中一些重要贡献的一些补充。