Is the Riemann tensor derivable from a tensor potential?

Details Is the Riemann tensor derivable from a tensor potential? Is the Riemann tensor derivable from a tensor potential?

Sep 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984gregr..16..805m&link_type=abstract

General Relativity and Gravitation, Volume 16, Issue 9, pp.805-816

Physics

10

Gravitation Theory

Scientific paper

In recent years, following an earlier result of C. Lanczos concerning the representation of the Weyl tensor in arbitrary space-times, it has been conjectured that the Riemann tensor itself admits a linear representation in terms of the covariant derivatives of a suitable “potential” tensor of rank 3. This conjecture is shown to be false, at least for a class of spacetime geometries including several physically significant ones.

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