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On the automorphism group of a closed G$_2$-structure (1801.06674v1)
Published 20 Jan 2018 in math.DG
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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