Half-flat structures on S^3xS^3

Abstract

We describe left-invariant half-flat SU(3)-structures on S^3xS^3 using the representation theory of SO(4) and matrix algebra. This leads to a systematic study of the associated cohomogeneity one Ricci-flat metrics with holonomy G_2 obtained on 7-manifolds with equidistant S^3xS^3 hypersurfaces. The generic case is analysed numerically.

23 pages, 6 figures. To appear in Annals of Global Analysis and Geometry

References in corpus (2)

• On the central quadric ansatz: integrable models and Painleve reductions
• SU(3)-holonomy metrics from nilpotent Lie groups

Cited by in corpus (13)

• $SU(2{)}^2$-invariant $G_2$-instantons
• Generalized Killing spinors on Einstein manifolds
• Generalized Killing spinors on spheres
• Coupled SU(3)-structures and Supersymmetry
• Left-invariant Einstein metrics on $S^3\times S^3$
• Half-flat structures inducing Einstein metrics on homogeneous spaces
• $G_2$-instantons on the spinor bundle of the 3-sphere
• Closed $\text{SL}(3,\mathbb{C})$-structures on nilmanifolds
• Some remarks on strong ${\mathrm{G}}_2$-structures with torsion
• Gravity and induced matter on Nearly Kahler Manifolds
• New examples of $G_2$-instantons on ${\mathbb{R}}^4\times S^3$
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds
• $G_2$-instantons on the ALC members of the ${\mathbb{B}}_7$ family