Extrinsic curvature refers to the curvature of a surface embedded in a higher-dimensional space. It is a measure of how the surface bends within that ambient space, contrasting with intrinsic curvature, which only considers properties of the surface itself. Understanding extrinsic curvature is essential in relating the geometry of a surface to the surrounding environment, and it's particularly relevant when discussing the Gauss and Codazzi equations.
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