Geometry and holonomy of indecomposable cones
Dmitri V. Alekseevsky
Institute for Information Transmission Problems, Moscow, Russia; University of Hradec Králové, Czech RepublicVicente Cortés
Universität Hamburg, GermanyThomas Leistner
University of Adelaide, Australia
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Abstract
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 -planes, and we study the cases 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 .
Cite this article
Dmitri V. Alekseevsky, Vicente Cortés, Thomas Leistner, Geometry and holonomy of indecomposable cones. Rev. Mat. Iberoam. 39 (2023), no. 3, pp. 1105–1141
DOI 10.4171/RMI/1330