Half-flat structures on S^3xS^3

Published 29 Nov 2012 in math.DG and hep-th | (1211.6845v2)

Abstract: We describe left-invariant half-flat SU(3)-structures on S^3xS³ 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^3xS³ hypersurfaces. The generic case is analysed numerically.

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