Locally conformal calibrated G₂-manifolds

2015/04/17 by Marisa Fernández, Fernández, Marisa, Anna Fino +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1504.04508

openalex publication_date 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conditions for which the mapping torus of a 6-manifold endowed with an SU(3)-structure is a locally conformal calibrated G₂-manifold, that is, a 7-manifold endowed with a G₂-structure φ such that d φ= - θ\wedge φ for a closed non-vanishing 1-form θ. Moreover, we show that if (M, φ) is a compact locally conformal calibrated G₂-manifold with L_θ^# φ=0, where θ^# is the dual of θ with respect to the Riemannian metric g_φ induced by φ, then M is a fiber bundle over S¹ with a coupled SU(3)-manifold as fiber.

Citations

• Non-formal co-symplectic manifolds

Related

• Conformal equivalence between certain geometries in dimension 6 and 7
• Calibrated Fibrations
• Manifolds admitting a G₂-structure
• Closed G2-structures with conformally flat metric
• The intrinsic torsion of SU(3) and G₂ structures