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arXiv · 1609.02747

Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures

Maciej Dunajski·Paul Tod
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Abstract

Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non--diagonal Bianchi type VIII Einstein metrics with self--dual Weyl tensor.

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Maciej Dunajski, Paul Tod. 2016-09-09. Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures. https://arxiv.org/abs/1609.02747

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