Nearly half-flat \rmSU(3)-structures on S³× S³

2023/10/17 by Ragini Singhal, Singhal, Ragini
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2310.11233

Abstract

We study the \rmSU(3)-structure induced on an oriented hypersurface of a 7-dimensional manifold with a nearly parallel \rmG₂-structure. We call such \rmSU(3)-structures nearly half-flat. We characterise the left invariant nearly half-flat structures on S³× S³. This characterisation then help us to systematically analyse nearly parallel \rmG₂-structures on an interval times S³× S³.

Related

• Lifting SU(3)-structures to nearly parallel G₂-structures
• SU(3)-structures on hypersurfaces of manifolds with G₂-structure
• Nearly parallel G₂-structures with large symmetry group
• Generalized G₂-manifolds and SU(3)-structures
• The intrinsic torsion of SU(3) and G₂ structures