General Relativity and Gravitation

, Volume 16, Issue 9, pp 805–816 | Cite as

Is the Riemann tensor derivable from a tensor potential?

  • Enrico Massa
  • Enrico Pagani
Research Articles


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.


Early Result Differential Geometry Covariant Derivative Linear Representation Weyl Tensor 
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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Enrico Massa
    • 1
  • Enrico Pagani
    • 1
  1. 1.Istituto Matematico dell'Università di GenovaGenovaItaly

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