Yang-Mills fields on quaternionic spaces. (English) Zbl 0681.53037
The authors extend to bundles over quaternionic Kähler manifolds the by now classical notion of self-duality over 4-dimensional spaces. This condition has a twistor interpretation in terms of twistors over quaternionic Kähler manifolds, a notion of the second author and L. Bérard Bergery. Interesting examples of self-dual connections over projective quaternionic spaces are constructed using an extension of the monad construction of Atiyah-Hitchin-Manin-Drinfeld.
Reviewer: J.P.Bourguignon
MSC:
53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
53C05 | Connections (general theory) |