2012/01/18 by Radu Pantilie, Pantilie, Radu · 1 citation
Mathematics · #53C28 (Primary) 53C26 (Secondary) #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C26 #msc:53C28
paper · pdf · doi:10.48550/arxiv.1201.3870
11 pages, improved version
openalex publication_date 2012/01/18 · arxiv created 2013/12/10 · arxiv updated 2013/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.