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:
“Civilisation is hooped together, brought
Under a rule, under the semblance of peace
By manifold illusion....”
—William Butler Yeats (1865–1939)