A smooth manifold M = (M, g) is said to be semi-Riemannian if the indexMetric Tensor Index of g is nonzero. Alternatively, a smooth manifold is semi-Riemannian provided that it comes equipped with a semi-Riemannian metric. In nearly all literature, the term semi-Riemannian is used synonymously with the term pseudo-Riemannian and is used to describe manifolds whose metric tensor g fails to be positive definite.
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