On a new normalization for tractor covariant derivatives

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10129033" target="_blank" >RIV/00216208:11320/12:10129033 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14310/12:00064347

Výsledek na webu

<a href="http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5" target="_blank" >http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4171/JEMS/349" target="_blank" >10.4171/JEMS/349</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On a new normalization for tractor covariant derivatives

Popis výsledku v původním jazyce

A regular normal parabolic geometry of type $G/P$ on a manifold $M$ gives rise to sequences $D_i$ of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative$na^om$ on the corresponding tractor bundle $V,$ where $om$ is the normal Cartan connection. The first operator $D_0$ in the sequence is overdetermined and it is well known that $na^om$ yields the prolongation of this operator in the homogeneous case $M = G/P$. Our first main result is the curved version of such a prolongation. This requires a new normalization $tilde{na}$ of the tractor covariant derivative on $V$. Moreover, we obtain an analogue for higher operators $D_i$. In that case one needs to modify the exterior covariant derivative $d^{na^om}$ by differential terms. Finally we demonstrate these results on simple examples in projective and Grassmannian geometry. Our approach is based on standard techniques of the BGG m

Název v anglickém jazyce

On a new normalization for tractor covariant derivatives

Popis výsledku anglicky

A regular normal parabolic geometry of type $G/P$ on a manifold $M$ gives rise to sequences $D_i$ of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative$na^om$ on the corresponding tractor bundle $V,$ where $om$ is the normal Cartan connection. The first operator $D_0$ in the sequence is overdetermined and it is well known that $na^om$ yields the prolongation of this operator in the homogeneous case $M = G/P$. Our first main result is the curved version of such a prolongation. This requires a new normalization $tilde{na}$ of the tractor covariant derivative on $V$. Moreover, we obtain an analogue for higher operators $D_i$. In that case one needs to modify the exterior covariant derivative $d^{na^om}$ by differential terms. Finally we demonstrate these results on simple examples in projective and Grassmannian geometry. Our approach is based on standard techniques of the BGG m

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/LC505" target="_blank" >LC505: Centrum Eduarda Čecha pro algebru a geometrii</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the European Mathematical Society

ISSN

1435-9855

e-ISSN

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Svazek periodika

2012

Číslo periodika v rámci svazku

14

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

25

Strana od-do

1859-1883

Kód UT WoS článku

000311877200005

EID výsledku v databázi Scopus

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