Pseudo-Riemannian manifold (source code)

= Pseudo-Riemannian manifold
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A <pseudo-Riemannian manifold> is a <smooth manifold> with a smooth <metric tensor> that is a <nondegenerate bilinear form> on each <tangent space>. Positivity is not required. A <Riemannian manifold> is the positive-definite case, while a <Lorentzian manifold> has exactly one temporal direction in its <metric signature>.