Given a pseudo-Riemannian manifold with metric tensor , its signature is the signature of as a quadratic form on any tangent space of , in the sense of signature of a quadratic form.
If is regarded as a model for spacetime, then this is also called spacetime signature.
Here the case of signature corresponds to Lorentzian geometry, being the basis of Einstein-gravity in the sense of “general relativity”.
The case of signature corresponds to Riemannian geometry (as opposed to pseudo-Riemannian). In a context of spacetime models this pertains for instance to the usual fibers in KK-compactifications, or to all of spacetime after “Wick rotation” (Euclidean gravity).
Spacetime signatures of the form have been considered in the context of D=12 supergravity and D=14 supersymmetry.
Created on November 28, 2020 at 12:53:22. See the history of this page for a list of all contributions to it.