On the twistor space of a (co-)CR quaternionic manifold

Abstract

We characterise, in the setting of the Kodaira-Spencer deformation theory, the twistor spaces of (co-)CR quaternionic manifolds. As an application, we prove that, locally, the leaf space of any nowhere zero quaternionic vector field on a quaternionic manifold is endowed with a natural co-CR quaternionic structure. Also, for any positive integers $k$ and $l$, with $kl$ even, we obtain the geometric objects whose twistorial counterparts are complex manifolds endowed with a conjugation without fixed points and which preserves an embedded Riemann sphere whose normal bundle is $l$ times the line bundle of Chern number $k$. We apply these results to prove the existence of natural classes of co-CR quaternionic manifolds.

11 pages, improved version

References in corpus (1)

• Twistor Theory for CR quaternionic manifolds and related structures

Cited by in corpus (2)

• On the embeddings of the Riemann sphere with nonnegative normal bundles
• On the integrability of the co-CR quaternionic structures