nLab
special holonomy table
classification of special holonomy manifolds by Berger's theorem:
| G-structure | special holonomy | dimension | preserved differential form |
---|
| Kähler manifold | U(n) | | Kähler forms |
| Calabi-Yau manifold | SU(n) | | |
| quaternionic Kähler manifold | Sp(n).Sp(1) | | |
| hyper-Kähler manifold | Sp(n) | | () |
| Spin(7) manifold | Spin(7) | 8 | Cayley form |
| G₂ manifold | G₂ | | associative 3-form |
Last revised on July 18, 2024 at 12:50:49.
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