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Let \(S\hookrightarrow (M,g)\) be an Riemannian submanifold . Then the normal space at some point \(p\in S\) is defined by

\begin{equation*} N_pS:=\{v\in T_pM: v\perp_gT_pS\}. \end{equation*}

We refer to \(NS=\bigcup_{p\in S} N_pS\) as normal bundle.

Remarks