Kaehler reduction of metrics with holonomy G_2

Abstract

A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations. Reversing the process in various special cases leads to the construction of explicit metrics with holonomy equal to G_2.

arXiv commentFinal version, to appear in Comm. Math. Phys

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Cited by in corpus (34)

• The Ricci tensor of SU(3)-manifolds
• Geometric Transitions, Flops and Non-Kahler Manifolds: II
• Generalised $G_2$-manifolds
• Multi-moment maps
• Special metric structures and closed forms
• SU(3)-instantons and $G_2,Spin(7)$-heterotic string solitons
• Hamiltonian symmetries and reduction in generalized geometry
• Nilmanifolds with a calibrated G_2-structure
• Calibrated cycles and T-duality
• G_2-structures with torsion from half-integrable nilmanifolds
• Sasakian Geometry, Holonomy, and Supersymmetry
• Einstein Metrics from Symmetry and Bundle Constructions: A Sequel
• Half-flat structures on S^3xS^3
• Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples
• New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities
• Spin(7)-manifolds with three-torus symmetry
• Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds
• $S^1$-invariant Laplacian flow
• Toric geometry of $G_2$-manifolds
• $S^1$-quotient of $Spin(7)$-structures
• Contact 5-manifolds with SU(2)-structure
• New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations
• Einstein metrics on bundles over hyperKähler manifolds
• Special Holonomy Manifolds, Domain Walls, Intersecting Branes and T-folds
• On generalized $G_2$-structures and $T$-duality
• Some remarks on strong ${\mathrm{G}}_2$-structures with torsion
• Complete Calabi-Yau metrics from Kahler metrics in D=4
• Mirror Duality via G_2 and Spin(7) Manifolds
• Explicit abelian instantons on $S^1$-invariant Kähler Einstein $6$-manifolds
• Special metrics in $G_2$ geometry
• Conformally parallel G_2 structures on a class of solvmanifolds
• Isolated singularities in $G_2$-structures with torsion
• On $G_2$-manifolds and geometry in dimensions $6$ and $8$
• Closed G${}_2$-structures on unimodular Lie algebras with non-trivial center