Gaussian curvature is a measure of the intrinsic curvature of a surface, defined at each point as the product of the principal curvatures. It captures how the surface bends in different directions and is essential for understanding the geometric properties of surfaces. This concept relates closely to Riemannian metrics, helping to characterize how distances and angles are measured on curved surfaces, and connects to sectional curvature, which describes curvature in a more general sense, highlighting its geometric implications.
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