Essential Parabolic Structures and Their Infinitesimal Automorphisms
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...
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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146856 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Essential Parabolic Structures and Their Infinitesimal Automorphisms / J. Alt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 14 назв. — англ. |
Репозитарії
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irk-123456789-1468562019-02-12T01:24:11Z Essential Parabolic Structures and Their Infinitesimal Automorphisms Alt, J. 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. 2011 Article Essential Parabolic Structures and Their Infinitesimal Automorphisms / J. Alt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 14 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53B05; 53C05; 53C17; 53C24 DOI:10.3842/SIGMA.2011.039 http://dspace.nbuv.gov.ua/handle/123456789/146856 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Alt, J. |
| spellingShingle |
Alt, J. Essential Parabolic Structures and Their Infinitesimal Automorphisms Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Alt, J. |
| author_sort |
Alt, J. |
| title |
Essential Parabolic Structures and Their Infinitesimal Automorphisms |
| title_short |
Essential Parabolic Structures and Their Infinitesimal Automorphisms |
| title_full |
Essential Parabolic Structures and Their Infinitesimal Automorphisms |
| title_fullStr |
Essential Parabolic Structures and Their Infinitesimal Automorphisms |
| title_full_unstemmed |
Essential Parabolic Structures and Their Infinitesimal Automorphisms |
| title_sort |
essential parabolic structures and their infinitesimal automorphisms |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146856 |
| citation_txt |
Essential Parabolic Structures and Their Infinitesimal Automorphisms / J. Alt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 14 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT altj essentialparabolicstructuresandtheirinfinitesimalautomorphisms |
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2023-05-20T17:25:52Z |
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2023-05-20T17:25:52Z |
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