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
140
167
28
Conti, D., Madsen, T. (2015). Invariant torsion and G2-metrics. COMPLEX MANIFOLDS, 2(1), 140-167 [10.1515/coma-2015-0011].
File in questo prodotto:
File Dimensione Formato  
invariant_geo.pdf

accesso aperto

Descrizione: Articolo principale
Dimensione 310.93 kB
Formato Adobe PDF
310.93 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/100837
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
Social impact