Null-geodesics in complex conformal manifolds and the LeBrun correspondence

Details Null-geodesics in complex conformal manifolds and the LeBrun correspondence Null-geodesics in complex conformal manifolds and the LeBrun correspondence

2000-02-26

arxiv.org/abs/math/0002225v1

Mathematics

Differential Geometry

17 pages, 1 figure, part of the paper is contained in (an old version of) the paper math.DG/0002029

Scientific paper

In the complex-Riemannian framework we show that a conformal manifold
containing a compact, simply-connected, null-geodesic is conformally flat. In
dimension 3 we use the LeBrun correspondence, that views a conformal 3-manifold
as the conformal infinity of a selfdual four-manifolds. We also find a relation
between the conformal invariants of the conformal infinity and its ambient.

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