English

On compact homogeneous $\mathrm{G}_{2(2)}$-manifolds

Differential Geometry 2019-09-10 v2

Abstract

We prove that among all compact homogeneous spaces for an effective transitive action of a Lie group whose Levi subgroup has no compact simple factors, the seven-dimensional flat torus is the only one that admits an invariant torsion-free G2(2)\mathrm{G}_{2(2)}-structure.

Cite

@article{arxiv.1808.10160,
  title  = {On compact homogeneous $\mathrm{G}_{2(2)}$-manifolds},
  author = {Wolfgang Globke},
  journal= {arXiv preprint arXiv:1808.10160},
  year   = {2019}
}

Comments

minor clarification in second (published) version

R2 v1 2026-06-23T03:48:51.414Z