A submanifold is a subset of a manifold that inherits a manifold structure of its own, allowing for the application of geometric and topological concepts within a lower-dimensional space. This concept is significant as it enables the analysis of properties of manifolds by studying these lower-dimensional spaces, often simplifying complex structures. Submanifolds can be either embedded, which means they sit nicely inside the larger manifold, or immersed, where they may not be globally flat but still maintain a manifold structure.
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