Half-flat structures on S^3xS^3
Thomas Bruun Madsen, Simon Salamon
TL;DR
This paper classifies left-invariant half-flat SU(3)-structures on S^3xS^3 using representation theory, and studies related Ricci-flat metrics with G_2 holonomy on 7-manifolds, including numerical analysis of the generic case.
Contribution
It provides a systematic description of half-flat structures on S^3xS^3 and explores associated Ricci-flat G_2 metrics, combining algebraic and numerical methods.
Findings
Classification of half-flat SU(3)-structures on S^3xS^3
Analysis of cohomogeneity one Ricci-flat G_2 metrics
Numerical results for the generic case
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.
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