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Statements

Subject Item

n2:RIV%2F00216224%3A14310%2F12%3A00064347%21RIV13-MSM-14310___

rdf:type

skos:Concept n17:Vysledek

rdfs:seeAlso

http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5

dcterms:description

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 $\nabla^\omega$ on the corresponding tractor bundle V, where $\omega$ is the normal Cartan connection. The first operator $D_0$ in the sequence is overdetermined and it is well known that $\nabla^\omega$ 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 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 $d^{\nabla^\omega}$ by differential terms. Finally we illustrate these results with simple examples in projective, conformal and Grassmannian geometry. Our approach is based on standard BGG techniques. 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 $\nabla^\omega$ on the corresponding tractor bundle V, where $\omega$ is the normal Cartan connection. The first operator $D_0$ in the sequence is overdetermined and it is well known that $\nabla^\omega$ 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 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 $d^{\nabla^\omega}$ by differential terms. Finally we illustrate these results with simple examples in projective, conformal and Grassmannian geometry. Our approach is based on standard BGG techniques.

dcterms:title

On a new normalization for tractor covariant derivatives On a new normalization for tractor covariant derivatives

skos:prefLabel

On a new normalization for tractor covariant derivatives On a new normalization for tractor covariant derivatives

skos:notation

RIV/00216224:14310/12:00064347!RIV13-MSM-14310___

n17:predkladatel

n18:orjk%3A14310

n3:aktivita

n6:Z n6:P

n3:aktivity

P(LC505), Z(MSM0021620839)

n3:cisloPeriodika

6

n3:dodaniDat

n10:2013

n3:domaciTvurceVysledku

n5:6901816

n3:druhVysledku

n13:J

n3:duvernostUdaju

n9:S

n3:entitaPredkladatele

n20:predkladatel

n3:idSjednocenehoVysledku

156164

n3:idVysledku

RIV/00216224:14310/12:00064347

n3:jazykVysledku

n21:eng

n3:klicovaSlova

Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry

n3:klicoveSlovo

n11:Parabolic%20geometry

n3:kodStatuVydavatele

CH - Švýcarská konfederace

n3:kontrolniKodProRIV

[F02C45E039E5]

n3:nazevZdroje

Journal of the European Mathematical Society

n3:obor

n15:BA

n3:pocetDomacichTvurcuVysledku

1

n3:pocetTvurcuVysledku

4

n3:projekt

n22:LC505

n3:rokUplatneniVysledku

n10:2012

n3:svazekPeriodika

14

n3:tvurceVysledku

Šilhan, Josef Hammerl, Matthias Somberg, Petr Souček, Vladimír

n3:wos

000311877200005

n3:zamer

n12:MSM0021620839

s:issn

1435-9855

s:numberOfPages

25

n4:doi

10.4171/JEMS/349

n19:organizacniJednotka

14310