A semi-Riemannian manifold M = (M, g) is said to be Lorentzian if dim(M)>=2 and if the index I = I_g associated with the metric tensor g satisfies I = 1. Alternatively, a smooth manifold M^n of dimension n>=2 is Lorentzian if it comes equipped with a tensor g of metric signature (1, n - 1) (or, equivalently, (n - 1, 1)).

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