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dc.contributor.author |
Alt, J. |
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dc.date.accessioned |
2019-02-11T17:22:22Z |
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dc.date.available |
2019-02-11T17:22:22Z |
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dc.date.issued |
2011 |
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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 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 53B05; 53C05; 53C17; 53C24 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2011.039 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/146856 |
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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 |
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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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