Ricci-Flat Holonomy: a Classification
arXiv:math/0602619 · doi:10.1016/j.geomphys.2006.12.003
Abstract
The reductive holonomy algebras for a torsion-free affine connection are analysed, with the goal of establishing which ones can correspond to a Ricci-flat connection with the same properties. Various families of holonomies are eliminated through different algebraic means, and examples are constructed (in this paper and in `Projective Geometry II: Holonomy Classification', by the same author) in the remaining cases, thus solving this problem completely, for reductive holonomy.
24 pages, slight corrections and presentation changes