Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures

Boris Doubrov*, Dennis The

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)25-44
    Number of pages20
    JournalDifferential Geometry and its Application
    Volume34
    DOIs
    Publication statusPublished - Jun 2014

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