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We give a short survey of the properties of Lanczos potential,
and we mention how this potential is relevant for the derivation
of the Weyl curvature tensor; we give some useful examples
that have been already computed elsewhere.
It was in 1962 when Cornelius Lanczos (1962) made the important
observation about that for any geometry, the Weyl conformal
curvature tensor, can be written as the covariant derivative
of a third rank tensor Labc, later called the
Lanczos potential. All attempts to generalize this result
for the case of the general curvature tensor of Riemann
have failed. Nevertheless, the Einstein equations can be
formulated in Jordan form and written in terms of the Weyl
tensor. Lanczos proved that the existence of a potential
for the general Riemann curvature tensor is not possible
and later Bampi and Caviglia gave a completely different
proof of this point (Bampi and Cavaglia, 1983). However,
they did not give a method to calculate the potential Labc.
Afterwards, Novello and Velloso (1987) showed a method to
compute the Lanczos potential tensor
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