2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71144Extending work of Chen, we prove the Weinstein conjecture in dimension three for strongly fillable contact structures with either non-vanishing first Chern class or with strong and exact filling having non-trivial canonical bundle. This implies the Weinstein conjecture for certain Stein fillable contact structures obtained by the Eliashberg-Gompf construction.For example we prove the Weinstein conjecture for the Brieskorn homology spheres $Σ(2,3,6n-1)$, $n\geq2$, oriented as the boundary of the corresponding Milnor fibre. Furthermore, for tight contact structures on odd lens spaces, non-contractible closed Reeb orbits are found.16 pages, latex2e, no figures, This third version coincides with the second one up to the following generalisation: The Weinstein conjecture holds true for the positively oriented Brieskorn homology spheres $Σ(2,3,6n-1)$, $n\geq2$Symplectic GeometryGeometric Topology53D35, 37J45text