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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2011, том 7, 039, 16 стр. (Mi sigma597)

Эта публикация цитируется в 4 статьях

Essential Parabolic Structures and Their Infinitesimal Automorphisms

Jesse Alt

School of Mathematics, University of the Witwatersrand, PO Wits 2050, Johannesburg, South Africa

Аннотация: 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.

Ключевые слова: essential structures; infinitesimal automorphisms; parabolic geometry; Lichnérowicz conjecture.

MSC: 53B05; 53C05; 53C17; 53C24

Поступила: 2 ноября 2010 г.; в окончательном варианте 11 апреля 2011 г.; опубликована 14 апреля 2011 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2011.039



Реферативные базы данных:
ArXiv: 1011.0288


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