2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229365Given a hyperelliptic Klein surface, we construct companion Klein bottles. Bavard's short loops on companion bottles are studied in relation to the surface to improve an inequality of Gromov's in systolic geometry.18 pages, 1 figureDifferential GeometryAlgebraic Geometry53C23; 30F10, 58J60text