Almost complex submanifolds of nearly Kähler manifolds
Résumé
We study almost complex submanifolds of pseudo nearly Kähler manifolds. We show in particular that a 6 dimensional strict nearly Kähler manifold does not admit any 4 dimensional almost complex submanifolds. This generalises results obtained by Gray (Proc Am Math Soc 20:277–279, 1969) for the nearly Kähler 6-sphere and by Podestà and Spiro (J Geom Phys 60:156–164, 2010) in the Riemannian case.