Geometry and holonomy of indecomposable cones

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dc.contributor.authorAlekseevsky, D.
dc.contributor.authorCortés, V.
dc.contributor.authorLeistner, T.
dc.date.issued2023
dc.description.abstractWe study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non-irreducible cones. The latter admit a parallel distribution of null k-planes, and we study the cases k = 1 in detail. We give structure theorems about the base manifold and in the case when the base manifold is Lorentzian, we derive a description of the cone holonomy. This result is obtained by a computation of certain cocycles of indecomposable subalgebras in so(1,n - 1).
dc.description.statementofresponsibilityDmitri Alekseevsky, Vicente Cortés and Thomas Leistner
dc.identifier.citationRevista Matematica Iberoamericana, 2023; 39(3):1105-1141
dc.identifier.doi10.4171/rmi/1330
dc.identifier.issn0213-2230
dc.identifier.issn2235-0616
dc.identifier.orcidLeistner, T. [0000-0002-8837-5215]
dc.identifier.urihttps://hdl.handle.net/2440/139844
dc.language.isoen
dc.publisherEMS Press - European Mathematical Society
dc.relation.granthttp://purl.org/au-research/grants/arc/FT110100429
dc.relation.granthttp://purl.org/au-research/grants/arc/DP190102360
dc.rights©2022 Real Sociedad Matemática Española. Published by EMS Press and licensed under a CC BY 4.0 license
dc.source.urihttps://doi.org/10.4171/rmi/1330
dc.titleGeometry and holonomy of indecomposable cones
dc.typeJournal article
pubs.publication-statusPublished

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