Cohomogeneity-one Einstein metrics on closed 4-manifolds
classification
🧮 math.DG
keywords
closedeinsteinmetricscohomogeneity-onemanifoldsmathbfclassifyconsequently
read the original 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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