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Bianchi type II, III and V diagonal Einstein metrics re-visited

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Abstract

We present, for both Minkowskian and Euclidean signatures, short derivations of the diagonal Einstein metrics for Bianchi type II, III and V. For the first two cases we show the integrability of the geodesic flow while for the third case a somewhat unusual bifurcation phenomenon takes place: for Minkowskian signature elliptic functions are essential in the metric while for Euclidean signature only elementary functions appear.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et des Hautes Energies, CNRS, UMR 7589, 2 Place Jussieu, 75251, Paris Cedex 05, France

    Galliano Valent

  2. Département de Mathématiques, UFR Sciences-Luminy, Case 901, 163 Avenue de Luminy, 13258, Marseille Cedex 9, France

    Galliano Valent

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  1. Galliano Valent
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Correspondence to Galliano Valent.

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Valent, G. Bianchi type II, III and V diagonal Einstein metrics re-visited. Gen Relativ Gravit 41, 2433–2459 (2009). https://doi.org/10.1007/s10714-009-0774-1

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  • DOI: https://doi.org/10.1007/s10714-009-0774-1

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