On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
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DOI：
10.1002/cpa.3160310304
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发表时间：
1978-05
影响因子：
3
通讯作者：
S. Yau
中科院分区：
文献类型：
--
作者：
S. Yau
因此，（1，l）形式（g i a'r r）i ,, rlr dz'a d？要成为某种卡勒度量的Ricci形式是必须关闭它，并且其协同学类必须代表二十多年前的Chern类。 。这种猜想的卡拉比可以简化为非线性部分微分方程中的问题。
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.