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The hyperkähler manifolds. (English) Zbl 0979.53051
Séminaire Bourbaki, Vol. 1991/92. Exposés 745-759 (avec table par noms d’auteurs de 1948/49 à 1991/92). Paris: Société Mathématique de France, Astérisque. 206, 137-166 (Exp. No. 748) (1992).
Summary: The concept of a hyper-Kähler manifold provides a means of introducing the algebra of quaternions into differential geometry. For a long time, there were few nontrivial examples, but through various constructions the subject has in recent years developed enormously, and one may now find naturally occurring hyper-Kähler manifolds in many different contexts, including the resolution of singularities, coadjoint orbits of complex Lie groups, and moduli spaces of connections.
For the entire collection see [Zbl 0772.00016].

MSC:
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
32S25 Complex surface and hypersurface singularities
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C28 Twistor methods in differential geometry
32L25 Twistor theory, double fibrations (complex-analytic aspects)
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