An embedded \(n\)-submanifold \(S\) of a \(m\)-manifold \(M\) suffices the slice condition, which is saying that on M an atlas exists such that for every chart \((\varphi, U)\) in that atlas

\[ S\cap \varphi(U) = \varphi(U\cap \mathbb{R}^n). \]

This induces a smooth structure on \(S\). [1, Theorem 5.8]

See also Link to heading

• embedded submanifold
• smooth coordinates
• smooth structure

References Link to heading

1. J. Lee, Introduction to Smooth Manifolds. New York ; London: Springer, 2013.