New York Journal of Mathematics
Volume 20 (2014) 959-971


Radu Pantilie

On the twistor space of a (co-)CR quaternionic manifold

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Published: October 27, 2014
Keywords: Twistor theory, quaternionic geometry
Subject: Primary 53C28, Secondary 53C26

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 with normal bundle lO(k).

We apply these results to prove the existence of natural classes of co-CR quaternionic manifolds.


The author acknowledges partial financial support from the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project no. PN-II-ID-PCE-2011-3-0362.

Author information

Institutul de Matematică "Simion Stoilow'' al Academiei Române, C.P. 1-764, 014700, Bucureşti, România