Ricci‐flat deformations of metrics with exceptional holonomy | Zendy

Nordström Johannes | Zendy

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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.

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