Decomposable conformal holonomy in Riemannian signature | Zendy

Armstrong Stuart | Zendy; Leitner Felipe | Zendy

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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.

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