Essential Parabolic Structures and Their Infinitesimal Automorphisms
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Essential Parabolic Structures and Their Infinitesimal Automorphisms
|
|
| Creator |
Alt, J.
|
|
| 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.
|
|
| Date |
2019-02-11T17:22:22Z
2019-02-11T17:22:22Z 2011 |
|
| Type |
Article
|
|
| Identifier |
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 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|