Kähler manifold, hyper-Kähler manifold, quaternionic Kähler manifold
classification of special holonomy manifolds by Berger's theorem:
G-structure | special holonomy | dimension | preserved differential form | |
---|---|---|---|---|
$\mathbb{C}$ | Kähler manifold | U(k) | $2k$ | Kähler forms $\omega_2$ |
Calabi-Yau manifold | SU(k) | $2k$ | ||
$\mathbb{H}$ | quaternionic Kähler manifold | Sp(k)Sp(1) | $4k$ | $\omega_4 = \omega_1\wedge \omega_1+ \omega_2\wedge \omega_2 + \omega_3\wedge \omega_3$ |
hyper-Kähler manifold | Sp(k) | $4k$ | $\omega = a \omega^{(1)}_2+ b \omega^{(2)}_2 + c \omega^{(3)}_2$ ($a^2 + b^2 + c^2 = 1$) | |
$\mathbb{O}$ | Spin(7) manifold | Spin(7) | 8 | Cayley form |
G2 manifold | G2 | $7$ | associative 3-form |
Last revised on May 6, 2018 at 02:13:07. See the history of this page for a list of all contributions to it.