Isometric Representation of Lipschitz-Free Spaces over Simply Connected Riemannian Manifolds

We show that the Lipschitz-Free Space over a simply connected $n$-dimensional Riemannian manifold $M$ is isometrically isomorphic to a quotient of $L^1(M,TM)$, the integrable vector-valued sections on the manifold, if $M$ is either complete or lies isomorphically inside a complete manifold $N$. Two functions are deemed equivalent in this quotient space if their difference has distributional divergence zero.