Abstract
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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Work done under the aegis of the activity of the National Group for Mathematical Physics of the C.N.R.
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Massa, E., Pagani, E. Is the Riemann tensor derivable from a tensor potential?. Gen Relat Gravit 16, 805–816 (1984). https://doi.org/10.1007/BF00762934
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DOI: https://doi.org/10.1007/BF00762934