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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1977 May;74(5):1798–1799. doi: 10.1073/pnas.74.5.1798

Calabi's conjecture and some new results in algebraic geometry

Shing-Tung Yau 1
PMCID: PMC431004  PMID: 16592394

Abstract

We announce a proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold and then apply it to prove some new results in algebraic geometry and differential geometry. For example, we prove that the only Kähler structure on a complex projective space is the standard one.

Keywords: Kähler manifold, Chern class, Ricci tensor, complex structure

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

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