On second-order, divergence-free tensors

  title={On second-order, divergence-free tensors},
  author={Jos'e Navarro},
  journal={Journal of Mathematical Physics},
  • J. Navarro
  • Published 18 June 2013
  • Mathematics, Physics
  • Journal of Mathematical Physics
The aim of this paper is to describe the vector spaces of those second-order tensors on a pseudo-Riemannian manifold (i.e., tensors whose local expressions only involve second derivatives of the metric) that are divergence-free. 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… 
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