About: On a new normalization for tractor covariant derivatives

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=14&iss=6&rank=5
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. (en)
Title	On a new normalization for tractor covariant derivatives On a new normalization for tractor covariant derivatives (en)
skos:prefLabel	On a new normalization for tractor covariant derivatives On a new normalization for tractor covariant derivatives (en)
skos:notation	RIV/00216224:14310/12:00064347!RIV13-MSM-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC505), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Šilhan, Josef
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	156164
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/12:00064347
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry (en)
http://linked.open.../riv/klicoveSlovo	Parabolic geometry - prolongation of invariant PDE’s - BGG sequence - tractor covariant derivatives - projective geometry - conformal geometry - Grassmannian geometry
http://linked.open...odStatuVydavatele	CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV	[F02C45E039E5]
http://linked.open...i/riv/nazevZdroje	Journal of the European Mathematical Society
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Eduard Čech Center for Algebra and Geometry
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	14
http://linked.open...iv/tvurceVysledku	Souček, Vladimír Somberg, Petr Šilhan, Josef Hammerl, Matthias
http://linked.open...ain/vavai/riv/wos	000311877200005
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	1435-9855
number of pages	25 (xsd:int)
http://bibframe.org/vocab/doi	10.4171/JEMS/349
http://localhost/t...ganizacniJednotka	14310

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