Curvature equations are mathematical formulas that describe the curvature properties of a manifold or surface, capturing how it bends or deviates from being flat. These equations are crucial for understanding geometric structures and play a vital role in the analysis of the Riemann curvature tensor, which measures the intrinsic curvature of a space, as well as the second fundamental form and mean curvature, which relate to the extrinsic curvature of surfaces embedded in higher-dimensional spaces.
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