2013/05/14 by Radu Pantilie, Pantilie, Radu
Mathematics · Physics and Astronomy · #53C26 #53C28 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.DG #msc:53C26 #msc:53C28
paper · pdf · doi:10.48550/arxiv.1305.3124
16 pages, slightly strengthened version
openalex publication_date 2013/05/14 · arxiv created 2013/05/16 · arxiv updated 2013/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterise the integrability of any co-CR quaternionic structure in terms of the curvature and a generalized torsion of the connection. Also, we apply this result to obtain, for example, the following. (1) New co-CR quaternionic structures built on vector bundles over a quaternionic manifold M, whose twistor spaces are holomorphic vector bundles over the twistor space Z of M. Moreover, all the holomorphic vector bundles over Z, which are positive and isotypic when restricted to the twistor lines, are obtained this way. (2) Under generic dimensional conditions, any manifold endowed with an almost f-quaternionic structure and a compatible torsion free connection is, locally, a product of a hypercomplex manifold with some power of the space of imaginary quaternions.