Bundles of Weyl structures and invariant calculus for parabolic
geometries

D 2023

Bundles of Weyl structures and invariant calculus for parabolic geometries

ČAP, Andreas a Jan SLOVÁK

Základní údaje

Originální název

Bundles of Weyl structures and invariant calculus for parabolic geometries

Autoři

ČAP, Andreas (40 Rakousko) a Jan SLOVÁK (203 Česká republika, domácí)

Vydání

Rhode Island (USA), The Diverse World of PDEs : Geometry and Mathematical Physics, od s. 53-72, 20 s. 2023

Nakladatel

American Mathematical Society

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Odkazy

URL

Kód RIV

RIV/00216224:14310/23:00134301

Organizační jednotka

Přírodovědecká fakulta

ISBN

978-1-4704-7147-7

ISSN

DOI

http://dx.doi.org/10.1090/conm/788/15819

Klíčová slova anglicky

Cartan geometry; parabolic geometry; Weyl structures; connections; symmetry; differential operator

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 5. 4. 2024 14:54, Mgr. Marie Šípková, DiS.

Anotace

V originále

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 $\Upsilon$.

Návaznosti

GX19-28628X, projekt VaV

Název: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou

Investor: Grantová agentura ČR, Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou

Citovat

ČAP, Andreas a Jan SLOVÁK. Bundles of Weyl structures and invariant calculus for parabolic geometries. In Krasil′shchik I. S., Sossinsky A. B., Verbovetsky A. M. The Diverse World of PDEs : Geometry and Mathematical Physics. Rhode Island (USA): American Mathematical Society, 2023, s. 53-72. ISBN 978-1-4704-7147-7. Dostupné z: https://dx.doi.org/10.1090/conm/788/15819.

@inproceedings{2342381,
   author = {Čap, Andreas and Slovák, Jan},
   address = {Rhode Island (USA)},
   booktitle = {The Diverse World of PDEs : Geometry and Mathematical Physics},
   doi = {http://dx.doi.org/10.1090/conm/788/15819},
   editor = {Krasil′shchik I. S., Sossinsky A. B., Verbovetsky A. M.},
   keywords = {Cartan geometry; parabolic geometry; Weyl structures; connections; symmetry; differential operator},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Rhode Island (USA)},
   isbn = {978-1-4704-7147-7},
   pages = {53-72},
   publisher = {American Mathematical Society},
   title = {Bundles of Weyl structures and invariant calculus for parabolic geometries},
   url = {https://bookstore.ams.org/view?ProductCode=CONM/788},
   year = {2023}
}

TY  - JOUR
ID  - 2342381
AU  - Čap, Andreas - Slovák, Jan
PY  - 2023
TI  - Bundles of Weyl structures and invariant calculus for parabolic geometries
PB  - American Mathematical Society
CY  - Rhode Island (USA)
SN  - 9781470471477
KW  - Cartan geometry
KW  - parabolic geometry
KW  - Weyl structures
KW  - connections
KW  - symmetry
KW  - differential operator
UR  - https://bookstore.ams.org/view?ProductCode=CONM/788
N2  - 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 $\Upsilon$.
ER  -

ČAP, Andreas a Jan SLOVÁK. Bundles of Weyl structures and invariant calculus for parabolic geometries. In Krasil′shchik I. S., Sossinsky A. B., Verbovetsky A. M. \textit{The Diverse World of PDEs : Geometry and Mathematical Physics}. Rhode Island (USA): American Mathematical Society, 2023, s.~53-72. ISBN~978-1-4704-7147-7. Dostupné z: https://dx.doi.org/10.1090/conm/788/15819.

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