Bundles of Weyl structures and invariant calculus for parabolic geometries

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134301" target="_blank" >RIV/00216224:14310/23:00134301 - isvavai.cz</a>
Result on the web
<a href="https://bookstore.ams.org/view?ProductCode=CONM/788" target="_blank" >https://bookstore.ams.org/view?ProductCode=CONM/788</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/conm/788/15819" target="_blank" >10.1090/conm/788/15819</a>

Result language
angličtina
Original language name
Bundles of Weyl structures and invariant calculus for parabolic geometries
Original language description
For more than hundred years, various concepts were developed to understand the fields of geometric objects and invariant differential operators between them for conformal Riemannian and projective geometries. More recently, several general tools were presented for the entire class of parabolic geometries, i.e., the Cartan geometries modelled on homogeneous spaces $G/P$ with $P$ a parabolic subgroup in a semi-simple Lie group $G$. Similarly to conformal Riemannian and projective structures, all these geometries determine a class of distinguished affine connections, which carry an affine structure modelled on differential 1-forms $Upsilon$. They correspond to reductions of $P$ to its reductive Levi factor, and they are called the Weyl structures similarly to the conformal case. The standard definition of differential invariants in this setting is as affine invariants of these connections, which do not depend on the choice within the class. In this article, we describe a universal calculus which provides an important first step to determine such invariants. We present a natural procedure how to construct all affine invariants of Weyl connections, which depend only tensorially on the deformations $Upsilon$.
Czech name
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Czech description
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Project
<a href="/en/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopy and Homology Methods and Tools Related to Mathematical Physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
The Diverse World of PDEs : Geometry and Mathematical Physics
ISBN
9781470471477
ISSN
0271-4132
e-ISSN
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Number of pages
20
Pages from-to
53-72
Publisher name
American Mathematical Society
Place of publication
Rhode Island (USA)
Event location
Moscow
Event date
Dec 13, 2021
Type of event by nationality
CST - Celostátní akce
UT code for WoS article
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