Pseudo-Riemannian manifold

Summary

A pseudo-Riemannian manifold is a smooth manifold with a smoothly varying nondegenerate symmetric bilinear form on each tangent space, which need not be positive definite. It generalises a Riemannian manifold, where the form is positive definite. The most important case is a Lorentzian manifold, the setting of general relativity. Much of Riemannian geometry, such as the Levi-Civita connection, geodesics and curvature, works in this setting.