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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F09%3A00036930%21RIV11-MSM-14310___
rdf:type
skos:Concept n15:Vysledek
dcterms:description
By a classical theorem of Gallot (1979), a Riemannian cone over a complete Riemannian manifold is either flat or has irreducible holonomy. We consider metric cones with reducible holonomy over pseudo-Riemannian manifolds. First we describe the local structure of the base of the cone when the holonomy of the cone is decomposable. For instance, we find that the holonomy algebra of the base is always the full pseudo-orthogonal Lie algebra. One of the global results is that a cone over a compact and complete pseudo-Riemannian manifold is either flat or has indecomposable holonomy. Then we analyse the case when the cone has indecomposable but reducible holonomy, which means that it admits a parallel isotropic distribution. This analysis is carried out, first in the case where the cone admits two complementary distributions and, second for Lorentzian cones. We show that the first case occurs precisely when the local geometry of the base manifold is para-Sasakian and that of the cone is para-K\%22ahlerian. By a classical theorem of Gallot (1979), a Riemannian cone over a complete Riemannian manifold is either flat or has irreducible holonomy. We consider metric cones with reducible holonomy over pseudo-Riemannian manifolds. First we describe the local structure of the base of the cone when the holonomy of the cone is decomposable. For instance, we find that the holonomy algebra of the base is always the full pseudo-orthogonal Lie algebra. One of the global results is that a cone over a compact and complete pseudo-Riemannian manifold is either flat or has indecomposable holonomy. Then we analyse the case when the cone has indecomposable but reducible holonomy, which means that it admits a parallel isotropic distribution. This analysis is carried out, first in the case where the cone admits two complementary distributions and, second for Lorentzian cones. We show that the first case occurs precisely when the local geometry of the base manifold is para-Sasakian and that of the cone is para-K\%22ahlerian.
dcterms:title
Cones over pseudo-Riemannian manifolds and their holonomy Cones over pseudo-Riemannian manifolds and their holonomy
skos:prefLabel
Cones over pseudo-Riemannian manifolds and their holonomy Cones over pseudo-Riemannian manifolds and their holonomy
skos:notation
RIV/00216224:14310/09:00036930!RIV11-MSM-14310___
n4:aktivita
n14:S n14:P
n4:aktivity
P(LC505), S
n4:cisloPeriodika
635
n4:dodaniDat
n10:2011
n4:domaciTvurceVysledku
Alekseevsky, Dmitry Galaev, Anton
n4:druhVysledku
n12:J
n4:duvernostUdaju
n16:S
n4:entitaPredkladatele
n13:predkladatel
n4:idSjednocenehoVysledku
308051
n4:idVysledku
RIV/00216224:14310/09:00036930
n4:jazykVysledku
n9:eng
n4:klicovaSlova
Holonomy groups; pseudo-Riemannian cones; doubly warped products; para-Sasaki and para-Kahler structures
n4:klicoveSlovo
n7:Holonomy%20groups n7:para-Sasaki%20and%20para-Kahler%20structures n7:pseudo-Riemannian%20cones n7:doubly%20warped%20products
n4:kodStatuVydavatele
DE - Spolková republika Německo
n4:kontrolniKodProRIV
[69F08F225094]
n4:nazevZdroje
Journal für die reine und angewandte Mathematik
n4:obor
n6:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
4
n4:projekt
n8:LC505
n4:rokUplatneniVysledku
n10:2009
n4:svazekPeriodika
2009
n4:tvurceVysledku
Alekseevsky, Dmitry Leistner, Thomas Cortes, Vicente Galaev, Anton
n4:wos
000270732200002
s:issn
0075-4102
s:numberOfPages
47
n17:organizacniJednotka
14310