A C^infty (infinitely differentiable) manifold is said to be a submanifold of a C^infty manifold M^' if M is a subset of M^' and the identity map of M into M^' is an embedding.

See also

Embedding, Manifold, Subfield, Subspace

Cite this as:

Weisstein, Eric W. "Submanifold." From MathWorld--A Wolfram Web Resource.