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topology > algebraic topology > manifold > differentiable manifold > pseudo-Riemannian manifold
geometry > topological space > manifold > differentiable manifold > pseudo-Riemannian manifold
geometry > differential geometry > differentiable manifold > pseudo-Riemannian manifold
topology > differential topology > differentiable manifold > pseudo-Riemannian manifold

Preferred term

pseudo-Riemannian manifold  

Definition(s)

  • In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Pseudo-Riemannian_manifold)

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Related concept(s)

Synonym(s)

  • semi-Riemannian manifold

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http://data.loterre.fr/ark:/67375/PSR-WNF2W5WC-J

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