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Decomposable conformal holonomy in Riemannian signature
Author(s) -
Armstrong Stuart,
Leitner Felipe
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000055
Subject(s) - holonomy , mathematics , conformal map , gravitational singularity , pure mathematics , signature (topology) , invariant (physics) , ricci flat manifold , singularity , riemannian geometry , mathematical analysis , geometry , mathematical physics , curvature , scalar curvature
Via Cartan and tractor calculus there is an invariant notion of conformal holonomy. Similar to the deRham decomposition theorem of Riemannian geometry, there is a geometric decomposition theorem for conformal holonomy as well. This was established in 3 and 15,17. However, in general, conformal manifolds with decomposable holonomy exhibit singularities. In this paper we solve the singularity case, which is based on the S l ‐doubling construction of 20.