Conformal flatness, non-Abelian Kaluza-Klein and the Quaternions

Physics – Mathematical Physics

Scientific paper

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13 pages, no figures, minor typo corrections

Scientific paper

Maximally symmetric manifolds with holonomy in the unitary quaternionic group
Sp(d/4) emerge from the non-Abelian Kaluza-Klein reduction of conformally flat
spaces. Thus, 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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