Annali di Matematica Pura ed Applicata

, Volume 193, Issue 3, pp 633–641 | Cite as

Generalized quaternionic manifolds

Article

Abstract

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 \(M\).

Keywords

Quaternionic manifold Generalized complex structure Twistor space 

Mathematics Subject Classfication (1991)

53D18 53C26 53C28 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institutul de Matematică “Simion Stoilow” al Academiei RomâneBucharestRomania

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