About: Conformal Operators on Forms and Detour Complexes on Einstein Manifolds

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian signature); the cohomology spaces of these; conformally stable form spaces that we may view as spaces of conformal harmonics; operators that generalise Branson's Q-curvature; global pairings between differential form bundles that descend to cohomology pairings. Here we show that these operators, spaces, and the theory underlying them, simplify significantly on conformally Einstein manifolds. We give explicit formulae for all the operators concerned. The null spaces for these, the conformal harmonics, and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form Laplacian. For the case of non-Ricci flat spaces this applies in all signatures and without topological restrictions. For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian signature); the cohomology spaces of these; conformally stable form spaces that we may view as spaces of conformal harmonics; operators that generalise Branson's Q-curvature; global pairings between differential form bundles that descend to cohomology pairings. Here we show that these operators, spaces, and the theory underlying them, simplify significantly on conformally Einstein manifolds. We give explicit formulae for all the operators concerned. The null spaces for these, the conformal harmonics, and the cohomology spaces are expressed explicitly in terms of direct sums of subspaces of eigenspaces of the form Laplacian. For the case of non-Ricci flat spaces this applies in all signatures and without topological restrictions. (en)
Title	Conformal Operators on Forms and Detour Complexes on Einstein Manifolds Conformal Operators on Forms and Detour Complexes on Einstein Manifolds (en)
skos:prefLabel	Conformal Operators on Forms and Detour Complexes on Einstein Manifolds Conformal Operators on Forms and Detour Complexes on Einstein Manifolds (en)
skos:notation	RIV/00216224:14310/08:00027954!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(LC505), S
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2010
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	361020
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/08:00027954
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	conformal operators on forms; Detour complexes; complex harmonics; conformal pairing; global conformal invariants; eigenvalues of the Laplacian (en)
http://linked.open.../riv/klicoveSlovo	Detour complexes complex harmonics conformal operators on forms conformal pairing eigenvalues of the Laplacian global conformal invariants
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[E7E0EFED7394]
http://linked.open...i/riv/nazevZdroje	Communications in Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Eduard Čech Center for Algebra and Geometry
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	284
http://linked.open...iv/tvurceVysledku	Gover, Rod Šilhan, Josef
http://linked.open...ain/vavai/riv/wos	000260065100001
issn	0010-3616
number of pages	25 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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