Smooth parameterization inside a manifold factors through the inclusion of a submanifold?
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I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.
My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?
differential-geometry
asked Nov 20 at 20:53
D_S
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up vote
0
down vote
favorite
I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.
My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?
differential-geometry
asked Nov 20 at 20:53
D_S
13.1k51551
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.
My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?
differential-geometry
asked Nov 20 at 20:53
D_S
13.1k51551
I am reading about Stokes theorem and was thinking about how I could simplify the reduce the proof to the case of $n-1$ forms on an $n$-dimensional manifold.
My question is this: suppose $M$ is an $n$ dimensional smooth manifold, and $f: [0,1]^k rightarrow M$ is a smooth map, where $k leq n$. Does there exist $k$ dimensional (embedded) submanifold $N$ of $M$ which contains the image of $f$?
differential-geometry
differential-geometry
asked Nov 20 at 20:53
D_S
13.1k51551
asked Nov 20 at 20:53
D_S
13.1k51551
asked Nov 20 at 20:53
D_S
13.1k51551
asked Nov 20 at 20:53
D_S
13.1k51551
asked Nov 20 at 20:53
D_S
13.1k51551
13.1k51551
add a comment |
add a comment |
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