Sectional curvature is a measure of the curvature of a Riemannian manifold, defined at each point in terms of a two-dimensional plane section through that point. It captures how the geometry behaves when restricted to that specific plane and can indicate whether the manifold is locally shaped more like a sphere, a flat plane, or a hyperbolic surface. Understanding sectional curvature is crucial for analyzing the properties of non-Euclidean geometries and their applications in differential geometry.
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