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,b2(M)}. This implies the non-existence of compact homogeneous manifolds endowed with an invariant closed non-parallel G2-structure. We also discuss some relevant examples.
On the automorphism group of a closed G2-structure
Raffero, Alberto
2019-01-01
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,b2(M)}. This implies the non-existence of compact homogeneous manifolds endowed with an invariant closed non-parallel G2-structure. We also discuss some relevant examples.
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Podesta Raffero Automorphism closed G2 revised.pdf
Open Access dal 29/08/2019
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