On second-order, divergence-free tensors

  title={On second-order, divergence-free tensors},
  author={Jos{\'e} Manuel Muries Navarro},
This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result establishes isomorphisms between these spaces and certain spaces of tensors (at a point) that are invariant under the action of an orthogonal group. This result is valid for tensors with an arbitrary number of indices and symmetries among them and, in… CONTINUE READING
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