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arXiv · 1801.06674

On the automorphism group of a closed G$_2$-structure

Fabio Podestà·Alberto Raffero
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Abstract

We study the automorphism group of a compact 7-manifold $M$ endowed with a closed non-parallel G$_2$-structure, showing that its identity component is abelian with dimension bounded by min$\{6,b_2(M)\}$. This implies the non-existence of compact homogeneous manifolds endowed with an invariant closed non-parallel G$_2$-structure. We also discuss some relevant examples.

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Fabio Podestà, Alberto Raffero. 2018-01-20. On the automorphism group of a closed G$_2$-structure. https://doi.org/10.1093/qmath%2Fhay045

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