2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120555We consider the reduced twistor space $Z$ of an almost Hermitian manifold $M$, after O'Brian and Rawnsley (Ann. Global Anal. Geom., 1985). We concentrate on dimension 6. This space has a natural almost complex structure $\mathcal J$ associated to the canonical Hermitian connection. A necessary condition for the integrability of $\mathcal J$ on $Z$ is that the manifold belongs to the class $W_1 \oplus W_4$ of Gray, Hervella. In a second part, we then show that the almost Hermitian manifolds of type $W_1 \oplus W_4$ are all locally conformally nearly Kähler in dimension 6. Finally, $\mathcal J$ is integrable if and only if $M$ is locally conformal to the sphere $S^6$ or to a Bochner-flat Kähler manifold.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 Kähler if and only if it is globally conformally nearly Kähler)Differential Geometry53C15 ; 53C28 ; 53C10text