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.
Submanifold
See also
Embedding, Manifold, Subfield, SubspaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Submanifold." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Submanifold.html