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Undid revision 973776207 by User:Ramzuiv – I am reverting this because to "correct any mistakes" is not really feasible: the ideas of "difference in time" and "distance in space" on a manifold are ill-defined. I'll elaborate on talk. |
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Such a metric is called a '''pseudo-Riemannian metric'''. Applied to a vector field, the resulting scalar field value at any point of the manifold can be positive, negative or zero.
The signature of a pseudo-Riemannian metric is {{nowrap|(''p'', ''q'')}}, where both ''p'' and ''q'' are non-negative. The non-degeneracy condition together with continuity implies that ''p'' and ''q'' remain unchanged throughout the manifold (assuming it is connected).
==Lorentzian manifold<!--'Lorentzian manifold' and 'Lorentzian metric' redirect here-->==
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