Mathematische Zeitschrift

, Volume 252, Issue 4, pp 825-848

First online:

Conformally parallel G 2 structures on a class of solvmanifolds

  • Simon G. ChiossiAffiliated withInstitut für Mathematik der Humboldt-Universität
  • , Anna FinoAffiliated withDipartimento di Matematica, Università di Torino Email author 

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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.

Mathematics Subject Classification (2000)

Primary 53C10 Secondary 53C25 53C29 22E25