Invariant torsion and G_2-metrics

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.

35 pages. To appear in Complex Manifolds

References in corpus (1)

• Harmonic structures and intrinsic torsion

Cited by in corpus (1)

• Toric geometry of $G_2$-manifolds