A holonomy characterisation of Fefferman spaces

Details A holonomy characterisation of Fefferman spaces A holonomy characterisation of Fefferman spaces

2006-11-30

arxiv.org/abs/math/0611939v1

Ann. Global Analysis Geom. 38, no. 4 (2010) 399-412

Mathematics

Differential Geometry

AMSLaTeX, 15 pages

Scientific paper

10.1007/s10455-010-9220-6

We prove that Fefferman spaces, associated to non--degenerate CR structures of hypersurface type, are characterised, up to local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This condition can be equivalently expressed in terms of conformal holonomy. Extracting from this picture the essential consequences at the level of tensor bundles yields an improved, conformally invariant analogue of Sparling's characterisation of Fefferman spaces.

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