2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60061We study the special algebraic properties of alternating 3-forms in 6 and 7 dimensions and introduce a diffeomorphism-invariant functional on the space of differential 3-forms on a closed manifold M in these dimensions. Restricting the functional to closed forms in a fixed cohomology class, we find that a critical point which is generic in a suitable sense defines in the 6-dimensional case a complex threefold with trivial canonical bundle and in 7 dimensions a Riemannian manifold with holonomy G2. This approach gives a direct method of finding a local moduli space, with its special geometry, for these structures.38 pages, LateXDifferential GeometryHigh Energy Physics - TheoryAlgebraic Geometry14J32; 53C25; 58E15text