Premium
Ricci‐flat deformations of metrics with exceptional holonomy
Author(s) -
Nordström Johannes
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt036
Subject(s) - holonomy , mathematics , moduli space , manifold (fluid mechanics) , torsion (gastropod) , ricci curvature , pure mathematics , mathematical analysis , dimension (graph theory) , moduli , geometry , physics , curvature , mechanical engineering , medicine , surgery , quantum mechanics , engineering
Let G be one of the Ricci‐flat holonomy groups SU( n ), Sp( n ), Spin(7) or G 2 , and M a compact manifold of dimension 2 n , 4 n , 8 or 7, respectively. We prove that the natural map from the moduli space of torsion‐free G ‐structures on M to the moduli space of Ricci‐flat metrics is open, and that the image is a smooth manifold. For the exceptional cases G = Spin(7) and G 2 , we extend the result to asymptotically cylindrical manifolds.