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Invariant torsion and G2-metrics

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We introduce and study a notion of invariant intrinsic torsion geometrywhich appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S3. This space is foliated by sixdimensional hypersurfaces, each of which carries a particular type of SO(3)-structure; the intrinsic torsion is invariant under SO(3). The last condition is sufficient to imply local homogeneity of such geometries, and this allows us to give a classification. We close the circle by showing that the Bryant-Salamon metric is the unique complete metric with holonomy G2 that arises from SO(3)-structures with invariant intrinsic torsion.
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  • Dipartimento di Matematica e Applicazioni, Universit`a di Milano Bicocca, Via Cozzi 55, 20125 Milano, Italy
  • Department of Mathematics, Aarhus University, Ny Munkegade 118, Bldg 1530, 8000 Aarhus, Denmark
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