Calabi Conjecture
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Calabi conjecture was a conjecture about the existence of good metrics on complex manifolds, made by Calabi in about 1954. The conjecture was proven by Shing-Tung Yau in 1976. The Calabi conjecture states that a compact Kähler manifold has a unique Kähler metric in the same class whose Ricci form is any given 2-form representing the first Chern class. In particular if the first Chern class vanishes there is a unique Kähler metric in the same cla...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Calabi conjecture was a conjecture about the existence of good metrics on complex manifolds, made by Calabi in about 1954. The conjecture was proven by Shing-Tung Yau in 1976. The Calabi conjecture states that a compact Kähler manifold has a unique Kähler metric in the same class whose Ricci form is any given 2-form representing the first Chern class. In particular if the first Chern class vanishes there is a unique Kähler metric in the same class with vanishing Ricci curvature; these are called Calabi Yau manifolds. The Calabi conjecture is closely related to the question of which Kähler manifolds have Kähler Einstein metrics.
