Geometry and holonomy of indecomposable cones

We 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 latte...

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Bibliographic Details
Published inRevista matemática iberoamericana Vol. 39; no. 3; pp. 1105 - 1141
Main Authors Alekseevsky, Dmitri, Cortes, Vicente, Leistner, Thomas
Format Journal Article
LanguageEnglish
Spanish
Published European Mathematical Society Publishing House 01.06.2023
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Summary:We 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 \mathfrak{so}(1,n-1) .
ISSN:0213-2230
2235-0616
DOI:10.4171/RMI/1330