Cohomogeneity-one Einstein metrics on closed $4$-manifolds

Kyle Broder

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arXiv · 2605.24859

Cohomogeneity-one Einstein metrics on closed $4$-manifolds

Kyle Broder

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Abstract

We classify the Einstein metrics on closed 4-manifolds whose isometry group has dimension at least 3. Consequently, we show that the cohomogeneity-one Einstein metrics on a closed $4$-manifold are locally symmetric or homothetic to the Page metric on $\mathbf{CP}^2 \sharp \overline{\mathbf{CP}}^2$.

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Kyle Broder. 2026-05-24. Cohomogeneity-one Einstein metrics on closed $4$-manifolds. https://arxiv.org/abs/2605.24859

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