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Exact G$_2$-structures on compact quotients of Lie groups (2108.11664v2)
Published 26 Aug 2021 in math.DG
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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