2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70110This paper generalizes a rigidity result of complex hyperbolic spaces by M. Herzlich. We prove that an almost Hermitian spin manifold $(M,g)$ of real dimension $4n+2$ which is strongly asymptotic to $\hyp{\C}^{2n+1}$ and satisfies a certain scalar curvature bound must be isometric to the complex hyperbolic space. The fact that we do not assume $g$ to be Kähler reflects in the inequality for the scalar curvature.8 pages. submitted to Comm. Anal. GeomDifferential Geometry53C24;53C55text