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Riemannian submersions, four-manifolds and Einstein-Weyl geometry. (English) Zbl 0742.53014
Einstein-Weyl spaces are conformal manifolds satisfying a conformally invariant analogue of the Einstein equations. New examples of Einstein-Weyl manifolds are constructed via Riemannian submersions on circle bundles over compact Einstein manifolds of positive scalar curvature and on certain torus bundles over products of Kähler-Einstein manifolds. The twistor theory of Einstein-Weyl four manifolds is discussed and a certain subclass of such manifolds is classified. Obstructions to the existence of Einstein-Weyl structures on four manifolds are produced and examples where these are non-zero are given.
Reviewer: A.Swann (Odense)

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53A30 Conformal differential geometry (MSC2010)
32L25 Twistor theory, double fibrations (complex-analytic aspects)
53C12 Foliations (differential geometric aspects)
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