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:
“The Lord wrote it all down on the little slate
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Outward and visible indication of the plan within,
The complex, manifold involvedness of an individual creature”
—D.H. (David Herbert)