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Essential Parabolic Structures and Their Infinitesimal Automorphisms

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dc.contributor.author Alt, J.
dc.date.accessioned 2019-02-11T17:22:22Z
dc.date.available 2019-02-11T17:22:22Z
dc.date.issued 2011
dc.identifier.citation Essential Parabolic Structures and Their Infinitesimal Automorphisms / J. Alt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 14 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 53B05; 53C05; 53C17; 53C24
dc.identifier.other DOI:10.3842/SIGMA.2011.039
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/146856
dc.description.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. uk_UA
dc.description.sponsorship I am grateful to Charles Frances for discussions about the methods used in [8] and [10], and to Felipe Leitner for useful comments on an earlier version of the text. The anonymous referees made many helpful criticisms and suggestions; in particular, I am grateful for the suggestion to reformulate an earlier (equivalent) version of Definition 2.1 in terms of the action of an automorphism on the set of Weyl structures. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Essential Parabolic Structures and Their Infinitesimal Automorphisms uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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