2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77260In this paper we continue the investigation of Loday's Leibniz cohomology as a new invariant for differentiable manifolds. In particular the Leibniz coboundary of a k-tensor (in the sense of differential geometry) is computed in a local coordinate chart and then interpreted in terms of the calculus of variations. For example, the Leibniz coboundary of the metric two-tensor reduces to the first variation of arc length.19 pagesAlgebraic TopologyDifferential Geometry55, 53, 18text