1997/11/30 by S. Brian Edgar, A. Höglund, Anders Höglund · 21 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Differential (mechanical device) #Differential geometry #Dimension (graph theory) #Lanczos resampling #Lanczos tensor #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Tensor (intrinsic definition) #gr-qc
paper · pdf · doi:10.1023/a:1001951609641
published in General Relativity and Gravitation 32(12), 2307-2318 (Springer Science+Business Media) · 11 pages, LaTeX, Heavily revised April 2000
arxiv created 2000/04/25 · openalex publication_date 2000/12/01 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 non-trivial condition involving only Wabcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential Labc.