Invariant torsion and G2-metrics

Diego Conti; Thomas Bruun Madsen

Complex Manifolds (2015)

  • Volume: 2, Issue: 1, page 140-167, electronic only
  • ISSN: 2300-7443

Abstract

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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.

How to cite

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Diego Conti, and Thomas Bruun Madsen. "Invariant torsion and G2-metrics." Complex Manifolds 2.1 (2015): 140-167, electronic only. <http://eudml.org/doc/275875>.

@article{DiegoConti2015,
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.},
author = {Diego Conti, Thomas Bruun Madsen},
journal = {Complex Manifolds},
keywords = {Bryant-Salamon metric; spinor bundle; holonomy; invariant intrinsic torsion},
language = {eng},
number = {1},
pages = {140-167, electronic only},
title = {Invariant torsion and G2-metrics},
url = {http://eudml.org/doc/275875},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Diego Conti
AU - Thomas Bruun Madsen
TI - Invariant torsion and G2-metrics
JO - Complex Manifolds
PY - 2015
VL - 2
IS - 1
SP - 140
EP - 167, electronic only
AB - 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.
LA - eng
KW - Bryant-Salamon metric; spinor bundle; holonomy; invariant intrinsic torsion
UR - http://eudml.org/doc/275875
ER -

References

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