Tod, K. P. Cohomogeneity-one metrics with self-dual Weyl tensor. (English) Zbl 0827.53017 Huggett, Stephen (ed.), Twistor theory. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 169, 171-184 (1995). The author reviews spatially homogeneous (or more generally cohomogeneity-one) four-dimensional metrics with self-dual Weyl tensor, with special attention to Bianchi-type IX Einstein metrics. In particular, this provides a test of the “integrability metatheorem” for systems of ODE derived from systems of PDE: a problem solvable by the twistor construction should have the (global) PainlevĂ© property.For the entire collection see [Zbl 0803.00012]. Reviewer: S.Kichenassamy (Paris) Cited in 2 ReviewsCited in 12 Documents MSC: 53B30 Local differential geometry of Lorentz metrics, indefinite metrics 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory Keywords:twistors; spatially homogeneous metrics with self-dual Weyl tensor; Bianchi-type IX Einstein metrics × Cite Format Result Cite Review PDF