English

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

Differential Geometry 2026-05-26 v1

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 44-manifold are locally symmetric or homothetic to the Page metric on CP2CP2\mathbf{CP}^2 \sharp \overline{\mathbf{CP}}^2.

Keywords

Cite

@article{arxiv.2605.24859,
  title  = {Cohomogeneity-one Einstein metrics on closed $4$-manifolds},
  author = {Kyle Broder},
  journal= {arXiv preprint arXiv:2605.24859},
  year   = {2026}
}