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Calabi's Conjecture and Some New Results in Algebraic Geometry

Shing-Tung Yau
Proceedings of the National Academy of Sciences of the United States of America
Vol. 74, No. 5 (May, 1977), pp. 1798-1799
Stable URL: http://www.jstor.org/stable/67110
Page Count: 2
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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.

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