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Results tagged with semi-riemannian-geometry
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user 2622
Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.
1
vote
Accepted
Existence of transverse null vector bundle in a degenerate Lorentzian hypersurface
Note that $CH$ is complemented in $TH = CH \oplus SH$, with $SH$ some non-unique choice of complementary sub-bundle. Then the restricted metric on $SH$ is non-degenerate (of Riemannian signature). The …
- 21.5k
4
votes
Accepted
Tensor Field Decomposition in Space time
The class of Lorentzian manifolds that is best suited for this kind of question is that of globally hyperbolic ones. Analyzing the space of solutions of a hyperbolic PDE that does not satisfy an analo …
- 21.5k
4
votes
Accepted
Is any globally-hyperbolic manifold conformally equivalent to one with complete slices?
This is the original Nomizu-Ozeki article:
Nomizu, Katsumi; Ozeki, Hideki, The existence of complete Riemannian metrics, Proc. Am. Math. Soc. 12, 889-891 (1961). ZBL0102.16401.
Applying their proof …
- 21.5k
1
vote
Lower bound for domain of exponential map on Lorentzian manifolds
In Riemannian geometry, the largest such $r$ is the injectivity radius. And there are curvature based bounds for it. To make sense of such a radius in Lorentzian geometry, you need also some reference …
- 21.5k
12
votes
Hodge decomposition in Minkowski space
Willie's answer is of course correct. But the part that I think is most interesting in the physical context is only briefly mentioned in point 3. of the last paragraph. Let me expand on that.
The rel …
- 21.5k