A submanifold 
of a 
(infinitely differentiable) manifold 
is a 
manifold that is a subset
of 
and for which the identity
map of 
into 
is an embedding.
Submanifold
See also
Embedding, Manifold, Subfield, SubspaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Submanifold." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Submanifold.html