sectional_ricci_curvature_manifold_diameter.pdf
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Math230a (Fall 2025) Yum-Tong Siu 1 Sectional and Ricci Curvature, Variations of Arc-Length and Diameter of Riemannian Manifold §1. Sectional Curvature of Riemannian Manifold We motivate the introduction of the notion of sectional curvature of a Rie- mannian manifold from two considerations. One is the generalization of the Gauss curvature of a surface in R3 as a function at a point to the case of a Riemannian manifold when a 2-dimensional linear subspace of the tangent space at a point is specified. The other is the…
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