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MSC: 53C25 53C99 83C15 83C20Subject classification: Global analysis Analysis on manifolds General relativity Keyword: Scalar curvature a b s t r a c t We discuss a differential equation, whose unknowns are a function and a Riemannian metric. This equation occurs both in general relativity (static space times) and in the study of the space of Riemannian metrics on a manifold (singularities of the map from the space of metrics into the space of functions, which assigns to any metric its scalar curvature).