A pseudo-Riemannian manifold is a manifold which has a metric that is of the signature , as compared to a Riemannian manifold, which has a signature of all positive signs.
See alsoCampbell's Theorem, Minkowski Metric, Minkowski Space, Riemannian Manifold
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Weisstein, Eric W. "Pseudo-Riemannian Manifold." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Pseudo-RiemannianManifold.html