Twistor theory for co-CR quaternionic manifolds and related structures. (English) Zbl 1281.53051
The authors answer the question posed in the introduction – “is there a natural class of manifolds, endowed with twistorial structures, which contains both the quaternionic manifolds and the three-dimensional Einstein-Weyl spaces?” In the paper under review they introduce a non-metrical notion of co-CR quaternionic manifolds and investigate its twistorial properties. At the end of the paper the authors build a heaven space for quaterninonic-Kähler structure.
Reviewer: Witold Mozgawa (Lublin)
MSC:
| 53C28 | Twistor methods in differential geometry |
| 53C26 | Hyper-Kähler and quaternionic Kähler geometry, “special” geometry |
| 32L25 | Twistor theory, double fibrations (complex-analytic aspects) |
| 32V30 | Embeddings of CR manifolds |
Keywords:
CR quaternionic manifold; \(f\)-quaternionic; \(q\)-umblical; linear hypercomlex structure; dual pair; twistorReferences:
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