arXiv:1801.06674 Abstract | arXiv Analytics

arXiv:1801.06674 [math.DG]Abstract References Reviews Resources

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

Published 2018-01-20Version 1

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.

Comments: 5 pages

Categories: math.DG

Keywords: automorphism group, identity component, relevant examples, compact homogeneous manifolds, invariant closed non-parallel

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