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Almost complex submanifolds of nearly Kähler manifolds

Abstract : 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.
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Limiao Lin, Luc Vrancken, Anne Wijffels. Almost complex submanifolds of nearly Kähler manifolds. Archiv der Mathematik, Springer Verlag, 2020, 115 (3), pp.353-358. ⟨10.1007/s00013-020-01469-w⟩. ⟨hal-03722951⟩



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