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Line 58: After Riemannian manifolds, Lorentzian manifolds form the most important subclass of pseudo-Riemannian manifolds. They are important in applications of [[general relativity]]. A principal premise of general relativity is that [[spacetime]] can be modeled as a 4-dimensional Lorentzian manifold of signature (-1,-1,-1,1) or, equivalently, (1,-1,-1,-1). Unlike Riemannian manifolds with positive-definite metrics, an indefinite signature allows tangent vectors to be classified into ''timelike'', ''null'' or ''spacelike''. With a signature of {{nowrap\|(''p'', 1)}} or {{nowrap\|(1, ''q'')}}, the manifold is also locally (and possibly globally) time-orientable (see ''[[Causal structure]]''). ==Properties of pseudo-Riemannian manifolds==

Pseudo-Riemannian manifold: Difference between revisions