In mathematics, particularly in the field of differential geometry, a **submanifold** is a subset of a manifold that itself has the structure of a manifold, often with respect to the topology and differential structure induced from the larger manifold.
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A submanifold is a manifold sitting inside another manifold through an immersion or embedding. An embedded submanifold has the subspace topology and local coordinates in which it is a coordinate plane. Smooth transverse intersections are governed by the tangent spaces of the participating submanifolds.