Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 433

Null-geoNull-geodesics in complex conformal manifolds and the LeBrun correspondence.desics in complex conformal manifolds and the LeBrun correspondence.

Florin Alexandru Belgun

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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