Yau's Theorem is a significant result in differential geometry that states that a compact Kähler manifold admits a unique Kähler-Einstein metric if its first Chern class is positive. This theorem connects the realms of complex geometry and Riemannian geometry, highlighting the importance of curvature properties in the context of complex manifolds. It provides crucial insights into the study of geometric structures on Kähler manifolds and their implications for various branches of mathematics.
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