Pinched self-dual Weyl curvature on Einstein four-manifolds

Inyoung Kim

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arXiv · 2512.00825

Pinched self-dual Weyl curvature on Einstein four-manifolds

Inyoung Kim

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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.

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Inyoung Kim. 2025-11-30. Pinched self-dual Weyl curvature on Einstein four-manifolds. https://arxiv.org/abs/2512.00825

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