A pseudo-Riemannian manifold is a differentiable manifold equipped with a non-degenerate, smooth, symmetric metric tensor which, unlike a Riemannian metric, need not be positive-definite, but must be non-degenerate. Such a metric is called a pseudo-Riemannian metric and its values can be positive, negative or zero.
The signature of a pseudo-Riemannian metric is (p, q) where both p and q are non-negative.
Read more about Pseudo-Riemannian Manifold: Lorentzian Manifold, Properties of Pseudo-Riemannian Manifolds
Famous quotes containing the word manifold:
“As one who knows many things, the humanist loves the world precisely because of its manifold nature and the opposing forces in it do not frighten him. Nothing is further from him than the desire to resolve such conflicts ... and this is precisely the mark of the humanist spirit: not to evaluate contrasts as hostility but to seek human unity, that superior unity, for all that appears irreconcilable.”
—Stefan Zweig (18811942)