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BY 4.0 license Open Access Published by De Gruyter Open Access July 30, 2019

G2-metrics arising from non-integrable special Lagrangian fibrations

  • Ryohei Chihara EMAIL logo
From the journal Complex Manifolds


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).

MSC 2010: 53C10; 53C25; 53C38


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Received: 2019-03-29
Accepted: 2019-07-18
Published Online: 2019-07-30
Published in Print: 2019-01-01

© 2019 Ryohei Chihara, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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