pseudo-Riemannian manifold
C3971
concept
A pseudo-Riemannian manifold is a smooth manifold equipped with a nondegenerate, symmetric metric tensor of arbitrary signature that allows measurement of lengths and angles, including those with indefinite sign as in spacetime geometry.
All labels observed (9)
| Label | Occurrences |
|---|---|
| Lorentzian metric | 4 |
| Riemannian manifold | 4 |
| Lorentz–Kähler-type metric | 1 |
| Ricci-flat manifold | 1 |
| Riemannian surface | 1 |
| p-brane | 1 |
| pseudo-Riemannian manifold canonical | 1 |
| pseudo-Riemannian metric | 1 |
| type D Petrov spacetime | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: pseudo-Riemannian manifold
Generated description
A pseudo-Riemannian manifold is a smooth manifold equipped with a nondegenerate, symmetric metric tensor of arbitrary signature that allows measurement of lengths and angles, including those with indefinite sign as in spacetime geometry.
Instances (13)
| Instance | Via concept surface |
|---|---|
| Gödel metric | Lorentzian metric |
| Calabi–Yau manifold | Ricci-flat manifold |
| Kerr metric | Lorentzian metric |
| Reissner–Nordström metric | Lorentzian metric |
| Kähler manifold | Riemannian manifold |
| Minkowski metric η_{μν} | Lorentzian metric |
| Kerr–Newman black hole | type D Petrov spacetime |
| Fefferman metric in several complex variables | Lorentz–Kähler-type metric |
| Poincaré upper half-plane model | Riemannian manifold |
| M5-branes | p-brane |
| Minkowski space-time | — |
| Liouville surface | Riemannian surface |
| 4-sphere S^4 | Riemannian manifold |