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arXiv · 1903.00956

Einstein Metrics, Harmonic Forms, and Conformally Kaehler Geometry

Claude LeBrun
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Abstract

The author has elsewhere given a complete classification of those compact oriented Einstein 4-manifolds on which the self-dual Weyl curvature is everywhere positive in the direction of some self-dual harmonic 2-form. In this article, similar results are obtained when the self-dual Weyl curvature is everywhere non-negative in the direction of a self-dual harmonic 2-form that is transverse to the zero section of the bundle of self-dual 2-forms. However, this transversality condition plays an essential role in the story; dropping it leads one into wildly different territory where entirely different phenomena predominate.

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Claude LeBrun. 2019-03-03. Einstein Metrics, Harmonic Forms, and Conformally Kaehler Geometry. https://arxiv.org/abs/1903.00956

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