Decomposable conformal holonomy in Riemannian signature

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 manif...

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Bibliographic Details
Published in:Mathematische Nachrichten 2012-02, Vol.285 (2-3), p.150-163
Main Authors: Armstrong, Stuart, Leitner, Felipe
Format: Article
Language:English
Subjects:
53C25
53C29
almost Einstein structures
Cartan and tractor calculus
collapsing sphere products
Conformal geometry
conformal holonomy
MSC 53A30
normal conformal Killing forms
special Einstein products
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Summary: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 Sl‐doubling construction of 20.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201000055