Lifting SU(3)-structures to nearly parallel G₂-structures

2007/07/13 by Sebastian Stock, Stock, Sebastian
Mathematics · #53C10 #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.0707.2029

openalex publication_date 2007/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hitchin shows that half-flat SU(3)-structures on a 6-dimensional manifold M can be lifted to parallel G₂-structure on the product M×ℝ. We show that Hitchin's approach can also be used to construct nearly parallel G₂-structures by lifting so-called nearly half-flat structures. These SU(3)-structures are described by pairs (ω,ϕ) of stable 2- and 3-forms with dϕ=λω² for some λ∈ℝ∖\0\.

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