Comments on certain divergencefree tensor densities in a 3space
Abstract
It is well known that a necessary and sufficient condition for the conformal flatness of a threedimensional pseudoRiemannian manifold can be expressed in terms of the vanishing of a thirdorder tensor density concomitant of the metric which has contravariant valence 2. This was first discovered by Cotton in 1899. It is shown that Cotton's tensor density is not the EulerLagrange expression corresponding to a scalar density built from one metric tensor. This tensor density is shown to be uniquely characterized by its conformal properties coupled with the demand that it be differentiable for arbitrary metrics.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 September 1979
 DOI:
 10.1063/1.524289
 Bibcode:
 1979JMP....20.1905A
 Keywords:

 04.20.Cv;
 04.20.Fy;
 Fundamental problems and general formalism;
 Canonical formalism Lagrangians and variational principles