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Dave Futer
Dave Futer
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Suppose I have a smooth manifold $M$, and aan embedded $C^2$ submanifold $N \subset M$, of codimension at least 3. Does there exist, for every point $x \in N$, a smooth ($C^\infty$) hypersurface in a ball in $M$, which contains the portion of $N$ in that ball?

Suppose I have a smooth manifold $M$, and a $C^2$ submanifold $N \subset M$, of codimension at least 3. Does there exist, for every point $x \in N$, a smooth hypersurface in a ball in $M$, which contains the portion of $N$ in that ball?

Suppose I have a smooth manifold $M$, and an embedded $C^2$ submanifold $N \subset M$, of codimension at least 3. Does there exist, for every point $x \in N$, a smooth ($C^\infty$) hypersurface in a ball in $M$, which contains the portion of $N$ in that ball?

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Dave Futer
Dave Futer
  • 1.3k
  • 11
  • 21

C^2 submanifolds contained in a hypersurface

Suppose I have a smooth manifold $M$, and a $C^2$ submanifold $N \subset M$, of codimension at least 3. Does there exist, for every point $x \in N$, a smooth hypersurface in a ball in $M$, which contains the portion of $N$ in that ball?