2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68828We deal with compact Kähler manifolds $M$ acted on by a compact Lie group $K$ of isometries, whose complexification $K^\C$ has exactly one open and one closed orbit in $M$. If the $K$-action is Hamiltonian, we obtain results on the cohomology and the $K$-equivariant cohomology of $M$.9 pagesSymplectic Geometry53C57; 53D20text