A 
(infinitely differentiable) manifold is said to be a submanifold of a 
manifold 
if 
is a subset of 
and the identity map of
into 
is an embedding.
See also
Embedding, Manifold, Subfield, Subspace
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Cite this as:
Weisstein, Eric W. "Submanifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Submanifold.html