Article ID Journal Published Year Pages File Type
4606079 Differential Geometry and its Applications 2014 20 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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