Vector field as smooth embedding

  • Thread starter huyichen
  • Start date
29
0
We can show that any vector field V:M->TM(tangent bundle of M) is smooth embedding of M, but how do we show that these smooth embeddings are all smoothly homotopic? How to construct such a homotopy?
 
1,444
4
I do not know much about homotopy, but my guess is that for every p in M you smoothly connect X(p) to Y(p) using the straight line connecting V(p) and W(p) in the tangent vector space at p.
 
489
0
Yep, it's the straight line homotopy.
 

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