Classification of compact homogeneous spaces with invariant $G_2$-structures
Abstract
In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a $G$-invariant $\tilde G_2$-structure, where $G$ is a compact Lie group. There are many new examples with nontrivial fundamental group. We study a subclass of homogeneous spaces of high rigidity and low rigidity and show that they admit families of invariant coclosed $G_2$-structures (resp. $\tilde G_2$-structures).
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2009
- DOI:
- 10.48550/arXiv.0912.0169
- arXiv:
- arXiv:0912.0169
- Bibcode:
- 2009arXiv0912.0169V
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Representation Theory;
- 57M50;
- 57M60
- E-Print:
- final version, 24p