Geometry and holonomy of indecomposable cones
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2023
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Alekseevsky, D.
Cortés, V.
Leistner, T.
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Revista Matematica Iberoamericana, 2023; 39(3):1105-1141
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Dmitri Alekseevsky, Vicente Cortés and Thomas Leistner
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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 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).
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©2022 Real Sociedad Matemática Española. Published by EMS Press and licensed under a CC BY 4.0 license