Conformal flatness, non-Abelian Kaluza-Klein reduction and quaternions |
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Authors: | Paolo Maraner |
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Affiliation: | a School of Economics and Management, Free University of Bozen/Bolzano, via Sernesi 1, Bolzano, 39100, Italyb School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK |
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Abstract: | The non-Abelian Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions and signatures. The corresponding equations are particularly elegant when the internal space supports a global Killing parallelization. Assuming this imposes the generalized ‘spacetime’ to be maximally symmetric with holonomy in the unitary quaternionic group Sp(d/4). Recalling an analogous result for the complex case, we conclude that all special manifolds with constant properly ‘holonomy-related’ sectional curvature, are in natural correspondence with conformally flat, possibly non-Abelian, Kaluza-Klein spaces. |
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Keywords: | Kaluza-Klein theories Confromally flat manifolds Non-Abelian fields Quaternions |
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