Global decomposition of vector field on Riemannian manifolds along natural coordinates

Earlier we presented a decomposition of a vector field on Euclidean space as a sum of a gradient field and a field orthogonal to the radius vector. In this paper we construct an analogous decomposition for vector fields on a Riemannian manifold of nonpositive curvature. ation to nonlinear mechanics and irreversible thermodynamics is proposed.