2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149133We construct the odd symplectic structure and the equivariant even (pre)symplectic one from it on the space of differential forms on the Riemann manifold. The Poincare -- Cartan like invariants of the second structure define the equivariant generalizations of the Euler classes on the surfaces.5 pages. The introduction of the paper is revisedHigh Energy Physics - TheoryDifferential Geometrytext