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.

Conti, D., Madsen, T. (2015). Invariant torsion and G2-metrics. COMPLEX MANIFOLDS, 2(1), 140-167 [10.1515/coma-2015-0011].

Invariant torsion and G2-metrics

Conti, D;
2015

Abstract

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.
Articolo in rivista - Articolo scientifico
G2 metrics, invariant intrinsic torsion
English
2015
2
1
140
167
open
Conti, D., Madsen, T. (2015). Invariant torsion and G2-metrics. COMPLEX MANIFOLDS, 2(1), 140-167 [10.1515/coma-2015-0011].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/100837
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