Given a smooth embedded submanifold of codimension 1, i.e. it is a hypersurface, say $H \hookrightarrow M$, is it possible to show that there exists an open nbd. $U\supset H$ in $M$ s.t it is diffeomorphic to $H \times (-a,a)$ for some $a\in \mathbb R$?
Note 1. If needed, assume orientability of $H$; it seems that one might need a non-zero section of the normal bundle.
Note 2. A proof without the use of a riemannian metric is appreciated.
2026-03-25 11:25:32.1774437932
Extending a hypersurface to a foliation
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