Conformally parallel G_2 structures on a class of solvmanifolds

Details Conformally parallel G_2 structures on a class of solvmanifolds Conformally parallel G_2 structures on a class of solvmanifolds

2004-09-08

arxiv.org/abs/math/0409137v1

Mathematics

Differential Geometry

22 pages

Scientific paper

Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G_2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G_2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the corresponding non-homogeneous Ricci-flat metrics with holonomy contained in G_2. In the process we also find a new metric with exceptional holonomy.

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