Dimensional Reduction of Conformal Tensors and Einstein-Weyl Spaces

2007/08/31 by R. Jackiw, Roman Jackiw · 2 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.3842/sigma.2007.091

published as SIGMA 3 (2007), 091, 7 pages · This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

arxiv created 2007/09/21 · openalex publication_date 2007/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Conformal Weyl and Cotton tensors are dimensionally reduced by a Kaluza-Klein procedure. Explicit formulas are given for reducing from four and three dimensions to three and two dimensions, respectively. When the higher dimensional conformal tensor vanishes because the space is conformallly flat, the lower-dimensional Kaluza-Klein functions satisfy equations that coincide with the Einstein-Weyl equations in three dimensions and kink equations in two dimensions.

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• Einstein–Weyl from Kaluza–Klein
• Anisotropic Weyl symmetry and cosmology

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