G2-metrics arising from non-integrable special Lagrangian fibrations
We study special Lagrangian fibrations of SU(3)-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group G, we decompose such SU(3)-structures into triples of solder 1-forms, connection 1-forms and equivariant 3 × 3 positive-definite symmetric matrix-valued func...
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| Format: | article |
| Langue: | EN |
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De Gruyter
2019
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| Accès en ligne: | https://doaj.org/article/30e6d6303ba440a2a7a6d1e3325dec1c |
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| Résumé: | We study special Lagrangian fibrations of SU(3)-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group G, we decompose such SU(3)-structures into triples of solder 1-forms, connection 1-forms and equivariant 3 × 3 positive-definite symmetric matrix-valued functions on principal G-bundles over 3-manifolds. As applications, we describe regular parts of G2-manifolds that admit Lagrangian-type 3-dimensional group actions by constrained dynamical systems on the spaces of the triples in the cases of G = T3 and SO(3). |
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