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arXiv · 1905.03077

Nearly parallel $G_2$-structures with large symmetry group

Fabio Podestà
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Abstract

We prove the existence of a one-parameter family of nearly parallel $G_2$-structures on the manifold $S^3\times \mathbb R^4$, which are mutually non isomorphic and invariant under the cohomogeneity one action of the group $SU(2)^3$. This family connects the two locally homogeneous nearly parallel $G_2$-structures which are induced by the homogeneous ones on the sphere $S^7$.

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Fabio Podestà. 2019-05-08. Nearly parallel $G_2$-structures with large symmetry group. https://arxiv.org/abs/1905.03077

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