General Relativity and Gravitation

, Volume 15, Issue 4, pp 375–386 | Cite as

Third-order tensor potentials for the Riemann and Weyl tensors

  • Franco Bampi
  • Giacomo Caviglia
Research Articles


The representations of the Riemann and the Weyl tensors of a four-dimensional Riemannian manifold through covariant derivatives of third-order potentials are examined in detail. The Weyl tensor always admits a completely general representation whereas the Riemann tensor does not. Nevertheless there exists a class of Riemannian manifolds whose Riemann tensors may be calculated in terms of potentials; in this connection, specific examples are exhibited explicitly. The possibility of introducing gauges on the potentials is reexamined in connection with the previous result. New properties of the representations are also discussed.


Manifold General Representation Riemannian Manifold Differential Geometry Covariant Derivative 
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Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Franco Bampi
    • 1
  • Giacomo Caviglia
    • 1
  1. 1.Istituto Matematico dell'Università di GenovaGenovaItaly

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