Espace de twisteurs d'une variete presque hermitienne de dimension 6
Abstract
We consider the reduced twistor space of an almost Hermitian manifold , after O'Brian and Rawnsley (Ann. Global Anal. Geom., 1985). We concentrate on dimension 6. This space has a natural almost complex structure associated to the canonical Hermitian connection. A necessary condition for the integrability of on is that the manifold belongs to the class of Gray, Hervella. In a second part, we then show that the almost Hermitian manifolds of type are all locally conformally nearly K\"{a}hler in dimension 6. Finally, is integrable if and only if is locally conformal to the sphere or to a Bochner-flat K\"{a}hler manifold.
Keywords
Cite
@article{arxiv.math/0503150,
title = {Espace de twisteurs d'une variete presque hermitienne de dimension 6},
author = {Jean-Baptiste Butruille},
journal= {arXiv preprint arXiv:math/0503150},
year = {2007}
}
Comments
In french. Version 2. The paper has been abbreviated from 38 pages to 30. The proof of the actual lemma 5.2 has been precised. Three references were added : [3], [7] and mostly [9] (Cleyton, Ivanov, math.DG/0607487 : the authors completed our theorem 1 by proving that a 6-dimensional almost Hermitian manifold is locally conformally nearly K\"{a}hler if and only if it is globally conformally nearly K\"{a}hler)