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

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.

arXiv comment5 pages

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Cited by in corpus (9)

• Closed G${}_2$-structures on non-solvable Lie groups
• A new example of a compact ERP G2-structure
• $S^1$-invariant Laplacian flow
• A compact $G_2$-calibrated manifold with first Betti number $b_1=1$
• Harmonic $Sp(2)$-invariant $G_2$-structures on the $7$-sphere
• Moduli spaces of (co)closed ${\mathrm{G}}_2$-structures on nilmanifolds
• Special types of locally conformal closed G${}_2$-structures
• Closed G${}_2$-structures with a transitive reductive group of automorphisms
• On the existence of homogeneous solitons of gradient type for the G${}_2$-Laplacian flow