We study the automorphism group of a compact 7-manifold M endowed with a closed non-parallel G2-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 G2-structure.
On the automorphism group of a closed G2-structure / Fabio Podestà; Alberto Raffero. - In: QUARTERLY JOURNAL OF MATHEMATICS. - ISSN 0033-5606. - STAMPA. - 70:(2019), pp. 195-200. [10.1093/qmath/hay045]
On the automorphism group of a closed G2-structure
Fabio Podestà;RAFFERO, ALBERTO
2019
Abstract
We study the automorphism group of a compact 7-manifold M endowed with a closed non-parallel G2-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 G2-structure.
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