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The first page of "Calabi's Conjecture and some new results in algebraic geometry." The abstract reads: "ABSTRACT: We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kahler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kahler structure on a complex projective space is the standard one."

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The first page of "Calabi's Conjecture and some new results in algebraic geometry." The abstract reads: "ABSTRACT: We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kahler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kahler structure on a complex projective space is the standard one."
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Robert McNees (mcnees@mastodon.social)'s status on Tuesday, 04-Apr-2023 15:00:46 UTC Robert McNees
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Yau's proof of Calabi's conjecture came in 1977-78. An immediate consequence is the existence of Calabi-Yau manifolds, compact 6 dimensional (or 3 complex-dimensional) manifolds that admit a unique Ricci-flat metric Kähler metric.
https://www.pnas.org/doi/10.1073/pnas.74.5.1798
https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160310304

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