2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69496The fundamental group of a Riemannian manifold with $δ$-pinched negative curvature, $δ>1/4$, cannot be the fundamental group of a quasicompact Kähler manifold. The proof also implies that a non-uniform lattice in $F_{4(-20)}$ cannot be the fundamental group of a quasicompact Kähler manifold. We also construct examples in the spirit of Gromov-Thurston to show that our result is a non-trivial extension of the previously known result that a non-uniform lattice in real hyperbolic space in dimension at least 3 cannot be the fundamental group of a quasicompact Kähler manifold.Version with additional supplementary material to appear in Intern.J.MathDifferential GeometryAlgebraic Geometry14E20, 58E20text