On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*

  title={On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*},
  author={Shing-Tung Yau},
  journal={Communications on Pure and Applied Mathematics},
  • S. Yau
  • Published 1 May 1978
  • Mathematics
  • Communications on Pure and Applied Mathematics
Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent the first Chern class of M. More than twenty years ago, E. Calabi [3] conjectured that the above necessary condition is in fact sufficient. This conjecture of Calabi can be reduced to a problem in non-linear partial differential equation. 
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