About: Cones over pseudo-Riemannian manifolds and their holonomy

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	Cones over pseudo-Riemannian manifolds and their holonomy Cones over pseudo-Riemannian manifolds and their holonomy (en)
skos:prefLabel	Cones over pseudo-Riemannian manifolds and their holonomy Cones over pseudo-Riemannian manifolds and their holonomy (en)
skos:notation	RIV/00216224:14310/09:00036930!RIV11-MSM-14310___
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(LC505), S
http://linked.open...iv/cisloPeriodika	635
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Galaev, Anton Alekseevsky, Dmitry
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	308051
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/09:00036930
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Holonomy groups; pseudo-Riemannian cones; doubly warped products; para-Sasaki and para-Kahler structures (en)
http://linked.open.../riv/klicoveSlovo	Holonomy groups doubly warped products para-Sasaki and para-Kahler structures pseudo-Riemannian cones
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[69F08F225094]
http://linked.open...i/riv/nazevZdroje	Journal für die reine und angewandte Mathematik
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (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	2009
http://linked.open...v/svazekPeriodika	2009
http://linked.open...iv/tvurceVysledku	Galaev, Anton Alekseevsky, Dmitry Leistner, Thomas Cortes, Vicente
http://linked.open...ain/vavai/riv/wos	000270732200002
issn	0075-4102
number of pages	47 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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