Title: Lectures on Differential Geometry Authors: Richard Schoen and Shing-Tung Yau Context: Graduate-level mathematics, Geometric Analysis, General Relativity
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Overall Rating: ⭐⭐⭐⭐½ (4.5/5) – Essential for the serious geometer, but not for beginners. schoen yau lectures on differential geometry pdf
The notes begin by moving beyond sectional curvature. While sectional curvature tells us about the geometry of 2D planes within a manifold, scalar curvature provides a "total" measure of curvature at a point. Schoen and Yau explore how this global invariant restricts the topology of the underlying manifold.