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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F08%3A00027954%21RIV10-MSM-14310___
rdf:type
skos:Concept n12:Vysledek
dcterms: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.
dcterms:title
Conformal Operators on Forms and Detour Complexes on Einstein Manifolds Conformal Operators on Forms and Detour Complexes on Einstein Manifolds
skos:prefLabel
Conformal Operators on Forms and Detour Complexes on Einstein Manifolds Conformal Operators on Forms and Detour Complexes on Einstein Manifolds
skos:notation
RIV/00216224:14310/08:00027954!RIV10-MSM-14310___
n3:aktivita
n18:S n18:P
n3:aktivity
P(LC505), S
n3:cisloPeriodika
2
n3:dodaniDat
n9:2010
n3:domaciTvurceVysledku
n13:6901816
n3:druhVysledku
n16:J
n3:duvernostUdaju
n14:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
361020
n3:idVysledku
RIV/00216224:14310/08:00027954
n3:jazykVysledku
n7:eng
n3:klicovaSlova
conformal operators on forms; Detour complexes; complex harmonics; conformal pairing; global conformal invariants; eigenvalues of the Laplacian
n3:klicoveSlovo
n8:conformal%20operators%20on%20forms n8:global%20conformal%20invariants n8:conformal%20pairing n8:Detour%20complexes n8:eigenvalues%20of%20the%20Laplacian n8:complex%20harmonics
n3:kodStatuVydavatele
NL - Nizozemsko
n3:kontrolniKodProRIV
[E7E0EFED7394]
n3:nazevZdroje
Communications in Mathematical Physics
n3:obor
n15:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n4:LC505
n3:rokUplatneniVysledku
n9:2008
n3:svazekPeriodika
284
n3:tvurceVysledku
Šilhan, Josef Gover, Rod
n3:wos
000260065100001
s:issn
0010-3616
s:numberOfPages
25
n10:organizacniJednotka
14310