A remark on conformal $\SU(p,q)$-holonomy

Details A remark on conformal $\SU(p,q)$-holonomy A remark on conformal $\SU(p,q)$-holonomy

2006-04-18

arxiv.org/abs/math/0604393v1

Mathematics

Differential Geometry

14 pages

Scientific paper

If the conformal holonomy group $Hol(\mathcal{T})$ of a simply connected space with conformal structure of signature $(2p-1,2q-1)$ is reduced to $\U(p,q)$ then the conformal holonomy is already contained in the special unitary group $\SU(p,q)$. We present two different proofs of this statement, one using conformal tractor calculus and an alternative proof using Sparling's characterisation of Fefferman metrics.

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