2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96715We give a procedure to ``average'' canonically $C^1$-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.Extention of results to non co-orientable contact manifolds (Section 5 added). 7 pagesSymplectic GeometryDifferential Geometry53D10text