# The Lanczos Potential for Weyl-Candidate Tensors Exists Only in Four Dimensions

@article{Edgar2000TheLP, title={The Lanczos Potential for Weyl-Candidate Tensors Exists Only in Four Dimensions}, author={S. Edgar and A. H{\"o}glund}, journal={General Relativity and Gravitation}, year={2000}, volume={32}, pages={2307-2318} }

We prove that a Lanczos potential Labc for the Weyl candidate tensor Wabcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for Labc and Wabcd, then this system's integrability conditions should be checked, and so on. When we find a… CONTINUE READING

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