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

Fabio Podestà; Alberto Raffero

doi:10.1093/qmath/hay045

paper

On the automorphism group of a closed G $_{2}$ -structure

arXiv:1801.06674 · doi:10.1093/qmath/hay045

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.

5 pages

References in corpus (3)

Laplacian Flow for Closed $G_{2}$ -Structures: Short Time Behavior
Cohomogeneity-one $G_{2}$ -Laplacian flow on 7-torus
Closed G $_{2}$ -structures on non-solvable Lie groups

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On the automorphism group of a closed G2​-structure

Abstract

References in corpus (3)

Cited by in corpus (9)

On the automorphism group of a closed G $_{2}$ -structure