Generalized Quaternionic Manifolds

Details Generalized Quaternionic Manifolds Generalized Quaternionic Manifolds

2011-09-29

arxiv.org/abs/1109.6475v3

Mathematics

Differential Geometry

10 pages, improved version

Scientific paper

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 $M$.

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