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On Pseudo-Riemannian Manifolds Whose Ricci Tensor is Parallel

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Abstract

Ricci-parallel Riemannian manifolds have a diagonal Ricci endomorphism Ric and are therefore, at least locally, a product of Einstein manifolds. This fails in the pseudo-Riemannian case. Using, on the one side, a general result in linear algebra due to Klingenberg and on the other side, a theorem on the holonomy of pseudo-Riemannian manifolds, this work classifies the different types of pseudo-Riemannian manifolds whose Ricci tensor is parallel.

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Authors and Affiliations

  1. Institut Elie Cartan, Unité Mixte de Recherche 7502 UHP, CNRS, INRIA, Université Henri Poincaré–Nancy I, BP 239, 54506, Vandœuvre-lès-Nancy Cedex, France

    Charles Boubel & Lionel Bérard Bergery

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  1. Charles Boubel
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  2. Lionel Bérard Bergery
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Boubel, C., Bergery, L.B. On Pseudo-Riemannian Manifolds Whose Ricci Tensor is Parallel. Geometriae Dedicata 86, 1–18 (2001). https://doi.org/10.1023/A:1011903507837

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  • DOI: https://doi.org/10.1023/A:1011903507837

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