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arXiv · 1911.13052

Closed G$_2$-structures with a transitive reductive group of automorphisms

Fabio Podestà·Alberto Raffero
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Abstract

We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G$_2$-structure and admitting a transitive reductive group G of automorphisms. In particular, we show that the center of G is one-dimensional and the manifold is the Riemannian product of a flat factor and a non-compact homogeneous six-dimensional manifold endowed with an invariant strictly symplectic half-flat SU(3)-structure.

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Fabio Podestà, Alberto Raffero. 2019-11-29. Closed G$_2$-structures with a transitive reductive group of automorphisms. https://doi.org/10.4310/ajm.2021.v25.n6.a6

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