Twistor Theory for CR quaternionic manifolds and related structures
arXiv:0905.1455 · doi:10.1007/s00605-011-0326-0
Abstract
In a general and non metrical framework, we introduce the class of CR quaternionic manifolds containing the class of quaternionic manifolds, whilst in dimension three it particularizes to, essentially, give the conformal manifolds. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain a heaven space construction for quaternionic manifolds.
arXiv commentThe paper has been split into two parts: 1. S. Marchiafava, L. Ornea, R. Pantilie, Twistor Theory for CR quaternionic manifolds and related structures; 2. S. Marchiafava, R. Pantilie, Twistor Theory for co-CR quaternionic manifolds and related structures. This is the first part. The second part will, also, be posted on the ArXiv; Monatshefte fuer Mathematik, 2011
References in corpus (2)
Cited by in corpus (13)
- Twistor Theory for CR quaternionic manifolds and related structures
- On the embeddings of the Riemann sphere with nonnegative normal bundles
- On holomorphic maps and Generalized Complex Geometry
- On the integrability of the co-CR quaternionic structures
- On the twistor space of a (co-)CR quaternionic manifold
- Generalized Quaternionic Manifolds
- Almost CR quaternionic manifolds and their immersibility in HP^n
- A generalized integrability problem for G-Structures
- Harmonic morphisms and moment maps on hyper-Kähler manifolds
- Quaternionic-like manifolds and homogeneous twistor spaces
- Cousin groups and Hodge structures
- (Pluri)harmonic morphisms and the Penrose-Ward transform
- Harmonic maps and twistorial structures