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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Autor principal:	Chihara Ryohei
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2019
Materias:	g-structures su(3)-structures g2-structures lagrangian fibrations einstein metrics 53c10 53c25 53c38 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/30e6d6303ba440a2a7a6d1e3325dec1c
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spelling	oai:doaj.org-article:30e6d6303ba440a2a7a6d1e3325dec1c2021-12-02T19:08:48ZG2-metrics arising from non-integrable special Lagrangian fibrations2300-744310.1515/coma-2019-0019https://doaj.org/article/30e6d6303ba440a2a7a6d1e3325dec1c2019-01-01T00:00:00Zhttps://doi.org/10.1515/coma-2019-0019https://doaj.org/toc/2300-7443We 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).Chihara RyoheiDe Gruyterarticleg-structuressu(3)-structuresg2-structureslagrangian fibrationseinstein metrics53c1053c2553c38MathematicsQA1-939ENComplex Manifolds, Vol 6, Iss 1, Pp 348-365 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	g-structures su(3)-structures g2-structures lagrangian fibrations einstein metrics 53c10 53c25 53c38 Mathematics QA1-939
spellingShingle	g-structures su(3)-structures g2-structures lagrangian fibrations einstein metrics 53c10 53c25 53c38 Mathematics QA1-939 Chihara Ryohei G2-metrics arising from non-integrable special Lagrangian fibrations
description	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).
format	article
author	Chihara Ryohei
author_facet	Chihara Ryohei
author_sort	Chihara Ryohei
title	G2-metrics arising from non-integrable special Lagrangian fibrations
title_short	G2-metrics arising from non-integrable special Lagrangian fibrations
title_full	G2-metrics arising from non-integrable special Lagrangian fibrations
title_fullStr	G2-metrics arising from non-integrable special Lagrangian fibrations
title_full_unstemmed	G2-metrics arising from non-integrable special Lagrangian fibrations
title_sort	g2-metrics arising from non-integrable special lagrangian fibrations
publisher	De Gruyter
publishDate	2019
url	https://doaj.org/article/30e6d6303ba440a2a7a6d1e3325dec1c
work_keys_str_mv	AT chihararyohei g2metricsarisingfromnonintegrablespeciallagrangianfibrations
_version_	1718377139319865344

G2-metrics arising from non-integrable special Lagrangian fibrations

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