Geometry and holonomy of indecomposable cones

• Dmitri V. Alekseevsky ^[3] ; Vicente Cortés ^[1] ; Thomas Leistner ^[2]
  1. [1] University of Hamburg

     University of Hamburg

     Hamburg, Freie und Hansestadt, Alemania

     
  2. [2] University of Adelaide

     University of Adelaide

     Australia

     
  3. [3] nstitute for Information Transmission Problems, Moscow, Russia; University of Hradec Králové, Czech Republic

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 3, 2023, págs. 1105-1141
• Idioma: inglés
• DOI: 10.4171/RMI/1330
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• Resumen

  • 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 D 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).