English

On Optimal 4-Dimensional Metrics

Differential Geometry 2007-11-13 v1 Complex Variables

Abstract

We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum of five reverse-oriented complex projective planes admits such metrics.

Keywords

Cite

@article{arxiv.0711.1668,
  title  = {On Optimal 4-Dimensional Metrics},
  author = {Claude LeBrun and Bernard Maskit},
  journal= {arXiv preprint arXiv:0711.1668},
  year   = {2007}
}

Comments

37 pages, 5 figures

R2 v1 2026-06-21T09:42:18.974Z