We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G2-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.
Closed G_2-structures with a transitive reductive group of automorphisms
Raffero, Alberto
2021-01-01
Abstract
We provide the complete classification of seven-dimensional manifolds endowed with a closed non-parallel G2-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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