2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143934We introduce a new class of zero-dimensional weighted complete intersections, by abstracting the essential features of rational cohomology algebras of equal rank homogeneous spaces of compact connected Lie groups. We prove that, on a 1-connected closed manifold M whose rational cohomology algebra belongs to this class, every isometry has a non-trivial invariant geodesic, for any metric on M. We use rational surgery to construct large classes of new examples for which the above result may be applied.14 pagesDifferential GeometryAlgebraic Topology53C22, 13C40 (primary); 57T15, 55P62, 57R65 (secondary)text