Calabi's conjecture and some new results in algebraic geometry

1977/05/01 by Shing–Tung Yau · 14 citations
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory #Differential geometry #Mathematics #Algebraic geometry #Manifold (fluid mechanics) #Conjecture #Complex projective space #Curvature #Pure mathematics #Differential (mechanical device) #Geometry #Algebraic number #Projective geometry #Space (punctuation) #Sectional curvature #Ricci curvature #Projective space #Algebra over a field #Scalar curvature #Physics #Mathematical analysis #Computer science #Projective test

paper · doi:10.1073/pnas.74.5.1798

openalex publication_date 1977/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

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.

Citations

• Characteristic Classes of Hermitian Manifolds

Cited by

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• A resolution of the sylvester-gallai problem of J.-P. serre
• Four-dimensional topology: an introduction
• 6D effective action of heterotic compactification on K3 with nontrivial gauge bundles
• Flux Backgrounds and Exceptional Generalised Geometry
• Kähler hyperbolic manifolds and Chern number inequalities
• On the Chern number inequalities satisfied by all smooth complete intersection threefolds with ample canonical class
• Shing-Tung Yau [wikipedia]