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.

Lorentzian manifold | metric signature | metric tensor | metric tensor index | positive definite tensor | pseudo-Euclidean space | pseudo-Riemannian manifold | semi-Riemannian metric | smooth manifold | strong pseudo-Riemannian metric | weak pseudo-Riemannian metric | weak Riemannian metric