  In 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.
