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Topics in four-dimensional Riemannian geometry. (English) Zbl 0532.53035
Geometry Semin. ”Luigi Bianchi”, Lect. Sc. Norm. Super., Pisa 1982, Lect. Notes Math. 1022, 33-124 (1983).
[For the entire collection see Zbl 0511.00021.]
This survey article gives a self-contained presentation of certain topics in 4-dimensional Riemannian geometry, centered around the concept of self-duality and the twistor space construction. The more recent results (Hitchin’s theorem on self-dual Einstein manifolds and sheaf cohomology properties of the twistor space) are discussed in Sections 10 and 11.
Reviewer: A.Derdzinski

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
32Q99 Complex manifolds
32C35 Analytic sheaves and cohomology groups