G2-metrics arising from non-integrable special Lagrangian fibrations

Abstract

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).

Keywords

• g-structures
• su(3)-structures
• g2-structures
• lagrangian fibrations
• einstein metrics
• 53c10
• 53c25
• 53c38