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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 039, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.039
(Mi sigma597)
 

This article is cited in 4 scientific papers (total in 4 papers)

Essential Parabolic Structures and Their Infinitesimal Automorphisms

Jesse Alt

School of Mathematics, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa
Full-text PDF (412 kB) Citations (4)
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Abstract: Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the generalized Ferrand–Obata theorem proved by C. Frances, this proves a generalization of the “Lichnérowicz conjecture” for conformal Riemannian, strictly pseudo-convex CR, and quaternionic/octonionic contact manifolds in positive-definite signature. For an infinitesimal automorphism with a singularity, we give a generalization of the dictionary introduced by Frances for conformal Killing fields, which characterizes (local) essentiality via the so-called holonomy associated to a singularity of an infinitesimal automorphism.
Keywords: essential structures; infinitesimal automorphisms; parabolic geometry; Lichnérowicz conjecture.
Received: November 2, 2010; in final form April 11, 2011; Published online April 14, 2011
Bibliographic databases:
Document Type: Article
Language: English
Citation: Jesse Alt, “Essential Parabolic Structures and Their Infinitesimal Automorphisms”, SIGMA, 7 (2011), 039, 16 pp.
Citation in format AMSBIB
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\by Jesse Alt
\paper Essential Parabolic Structures and Their Infinitesimal Automorphisms
\jour SIGMA
\yr 2011
\vol 7
\papernumber 039
\totalpages 16
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855223385}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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