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On the twistor space of a (co-)CR quaternionic manifold | | Radu Pantilie
; | | Date: |
18 Jan 2012 | | Abstract: | We characterise, in the setting of the Kodaira-Spencer deformation theory,
the twistor space of any (co-)CR quaternionic manifold. 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, we prove that there exists a natural correspondence between
the following classes: (i) complex surfaces endowed with a conjugation without
fixed points and which preserves an embedded Riemann sphere, and (ii)
quadruples (M,N,x,f) with xin Msubseteq N, and where N is quaternionic, M is
a generic submanifold of N, 2dimM=dimN+2, and f:N o M is a twistorial
retraction. Consequently, many large natural classes of quaternionic manifolds
are obtained by using rational ruled surfaces. | | Source: | arXiv, 1201.3870 | | Services: | Forum | Review | PDF | Favorites | |
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