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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 29, 2015

Invariant torsion and G2-metrics

  • Diego Conti and Thomas Bruun Madsen
From the journal Complex Manifolds


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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Received: 2015-6-23
Accepted: 2015-10-19
Published Online: 2015-10-29

© 2015 Diego Conti and Thomas Bruun Madsen

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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