Singular Self-dual Zollfrei Metrics and Twistor Correspondence

Details Singular Self-dual Zollfrei Metrics and Twistor Correspondence Singular Self-dual Zollfrei Metrics and Twistor Correspondence

2006-07-12

arxiv.org/abs/math/0607276v1

Mathematics

Differential Geometry

25pages

Scientific paper

10.1016/j.geomphys.2006.12.004

We construct examples of singular self-dual Zollfrei metrics explicitly, by patching a pair of Petean's self-dual split-signature metrics. We prove that there is a natural one-to-one correspondence between these singular metrics and a certain set of embeddings of $RP^3$ to $CP^3$ which has one singular point. This embedding corresponds to an odd function on $R$ that is rapidly decreasing and pure imaginary valued. The one-to-one correspondence is explicitly given by using the Radon transform.

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