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arXiv · 2108.11664

Exact G$_2$-structures on compact quotients of Lie groups

Anna Fino·Lucía Martín-Merchán·Alberto Raffero
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Abstract

We show that the compact quotient $\Gamma\backslash\mathrm{G}$ of a seven-dimensional simply connected Lie group $\mathrm{G}$ by a co-compact discrete subgroup $\Gamma\subset\mathrm{G}$ does not admit any exact $\mathrm{G}_2$-structure which is induced by a left-invariant one on $\mathrm{G}$.

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Anna Fino, Lucía Martín-Merchán, Alberto Raffero. 2021-08-26. Exact G$_2$-structures on compact quotients of Lie groups. https://doi.org/10.1007/s10231-022-01264-0

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