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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Збережено в:
Бібліографічні деталі
Дата:2011
Автор: Alt, J.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2011
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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
Резюме: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.