English

Pinched self-dual Weyl curvature on Einstein four-manifolds

Differential Geometry 2025-12-02 v1

Abstract

We show that a compact oriented riemannian four-manifold with harmonic and pinched self-dual Weyl curvature is anti-self-dual if the type is nonpositive. The main part is to show that there is an almost-K\"ahler structure outside the zero set of the self-dual Weyl curvature.

Keywords

Cite

@article{arxiv.2512.00825,
  title  = {Pinched self-dual Weyl curvature on Einstein four-manifolds},
  author = {Inyoung Kim},
  journal= {arXiv preprint arXiv:2512.00825},
  year   = {2025}
}