Classifier Instance:

Anchor text: Kähler manifold
Target Entity: K\u00e4hler_manifold
Preceding Context: By far the hardest part of proving the equivalences between the various properties above is proving the existence of Ricci-flat metrics. This follows from Yau's proof of the Calabi conjecture, which implies that a compact
Succeeding Context: with a vanishing first real Chern class has a Kähler metric in the same class with vanishing Ricci curvature. (The class of a Kähler metric is the cohomology class of its associated 2-form.) Calabi showed such a metric is unique.
Paragraph Title: Definitions
Source Page: Calabi–Yau manifold

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