2011/09/29 by Radu Pantilie, Pantilie, Radu
Mathematics · #53C26 #53C28 #53D18 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1109.6475
openalex publication_date 2011/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We initiate the study of the generalized quaternionic manifolds by classifying the generalized quaternionic vector spaces, and by giving two classes of nonclassical examples of such manifolds. Thus, we show that any complex symplectic manifold is endowed with a natural (nonclassical) generalized quaternionic structure, and the same applies to the heaven space of any three-dimensional Einstein-Weyl space. In particular, on the product Z of any complex symplectic manifold M and the sphere there exists a natural generalized complex structure, with respect to which Z is the twistor space of M.