A new construction of anti-self-dual four-manifolds (Q2638397)

The paper use twistor space construction to provide new local anti-self-dual metrics on four manifolds. The twistor spaces which the author considers are affine bundles over complex surfaces. He associates a five-dimensional manifold \textbf{Y} and a function \(V\) which satisfies a second order differential equation. Then the data determines a conformal anti-self dual structure on open set of \(\{V=0\}\). Details in the specific case when the twistor space projects over \(\mathbb{CP}^2\) are given. The twistor lines project onto a plane conies in this case.