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Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures

Doubrov, Boris; The, Dennis


We establish the submaximal symmetry dimension for Riemannian and Lorentzian conformal structures. The proof is based on enumerating all subalgebras of orthogonal Lie algebras of sufficiently large dimension and verifying if they stabilize a non-zero Weyl tensor up to scale. Our main technical tools include Dynkin's classification of maximal subalgebras in complex simple Lie algebras, a theorem of Mostow, and Kostant's Bott-Borel-Weil theorem.

CollectionsANU Research Publications
Date published: 2014
Type: Journal article
Source: Differential Geometry and its Applications
DOI: 10.1016/j.difgeo.2014.03.007


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