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arXiv · 2111.11361

Heisenberg-invariant self-dual Einstein manifolds

Vicente Cortés·Ángel Murcia
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Abstract

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can take any value. Then we study when the corresponding (Riemannian or neutral-signature) metrics are (geodesically) complete. Finally, we exhibit the solutions of non-zero Ricci-curvature as different branches of one-loop deformed universal hypermultiplets in Riemannian and neutral signature.

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Vicente Cortés, Ángel Murcia. 2021-11-22. Heisenberg-invariant self-dual Einstein manifolds. https://doi.org/10.1088/1361-6382%2Fac9bc4

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