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arXiv · 1410.6173

Invariant torsion and G_2-metrics

Diego Conti·Thomas Bruun Madsen
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Abstract

We introduce and study a notion of invariant intrinsic torsion geometry which appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S^3. This space is foliated by six-dimensional 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 G_2 that arises from SO(3)-structures with invariant intrinsic torsion.

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Diego Conti, Thomas Bruun Madsen. 2014-10-22. Invariant torsion and G_2-metrics. https://doi.org/10.1515/coma-2015-0011

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