Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures

Boris Doubrov; Dennis The

doi:10.1016/j.difgeo.2014.03.007

Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures

Boris Doubrov^*, Dennis The

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Pages (from-to)	25-44
Number of pages	20
Journal	Differential Geometry and its Application
Volume	34
DOIs	https://doi.org/10.1016/j.difgeo.2014.03.007
Publication status	Published - Jun 2014

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title = "Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures",

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.",

keywords = "Conformal geometry, Submaximal symmetry, Weyl tensor",

author = "Boris Doubrov and Dennis The",

year = "2014",

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doi = "10.1016/j.difgeo.2014.03.007",

language = "English",

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publisher = "Elsevier B.V.",

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T1 - Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures

AU - Doubrov, Boris

AU - The, Dennis

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

KW - Conformal geometry

KW - Submaximal symmetry

KW - Weyl tensor

UR - http://www.scopus.com/inward/record.url?scp=84898663778&partnerID=8YFLogxK

U2 - 10.1016/j.difgeo.2014.03.007

DO - 10.1016/j.difgeo.2014.03.007

M3 - Article

SN - 0926-2245

VL - 34

SP - 25

EP - 44

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

ER -

Maximally degenerate Weyl tensors in Riemannian and Lorentzian signatures

Abstract

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