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A SURVEY OF LANCZOS POTENTIAL

Rubén Sánchez Sánchez, César Mora

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Abstract

It was in 1962 when Cornelius Lanczos (1962) made the important observation about thet 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. Nevertheles, the Einstein equeations can be formulated in Jordan form and written in terms of the Weyl tensor.

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What this paper is about

It was in 1962 when Cornelius Lanczos (1962) made the important observation about thet 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. Nevertheles, the Einstein equeations can be formulated in Jordan form and written in terms of the Weyl tensor.

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Available abstract

It was in 1962 when Cornelius Lanczos (1962) made the important observation about thet 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. Nevertheles, the Einstein equeations can be formulated in Jordan form and written in terms of the Weyl tensor.

Key concepts: Lanczos tensor, Lanczos resampling, Weyl tensor, Covariant derivative, Riemann curvature tensor, Covariant transformation, Einstein tensor, Tensor (intrinsic definition)

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