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The Penrose transform on conformally Bochner-Kähler manifolds. (English) Zbl 1153.53032

This paper deals with the twistor correspondence of the Dolbeault complex over Hermitian manifolds whose metrics are locally conformally equivalent to Bochner Kähler metrics, called conformally Bochner Kähler manifolds. The author starts with the definition of twistor spaces of an almost Hermitian manifold and with a study of integrability conditions. After that some equations related to conformally Bochner Kähler manifolds are given. Finally the Penrose transform is defined and its surjectivity is proved.

MSC:

53C28 Twistor methods in differential geometry
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