The Tubular Neighborhood Theorem states that around every embedded submanifold of a Riemannian manifold, there exists a neighborhood that is diffeomorphic to a normal bundle. This theorem provides a way to visualize submanifolds within larger manifolds, allowing us to understand the geometry of the submanifold in relation to the ambient space. The theorem is fundamental for establishing properties such as the induced metric on the submanifold and understanding how local geometry behaves near the submanifold.
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