The second fundamental form is a mathematical tool used to describe the intrinsic curvature of a submanifold embedded in a Riemannian manifold. It captures how the submanifold bends within the ambient space and provides crucial information about its geometry, such as how it deviates from being flat. Understanding this concept is key when looking at examples of Riemannian manifolds, exploring the geometry induced on submanifolds, and analyzing properties like mean curvature.
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