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Complex Manifolds

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Invariant torsion and G2-metrics

Diego Conti
  • Corresponding author
  • Dipartimento di Matematica e Applicazioni, Universit`a di Milano Bicocca, Via Cozzi 55, 20125 Milano, Italy
  • Other articles by this author:
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/ Thomas Bruun Madsen
  • Corresponding author
  • Department of Mathematics, Aarhus University, Ny Munkegade 118, Bldg 1530, 8000 Aarhus, Denmark
  • Other articles by this author:
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Published Online: 2015-10-29 | DOI: https://doi.org/10.1515/coma-2015-0011

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.

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About the article

Received: 2015-06-23

Accepted: 2015-10-19

Published Online: 2015-10-29


Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0011.

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© 2015 Diego Conti and Thomas Bruun Madsen. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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