Differential 1 form on line

  • #1
Abhishek11235
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Homework Statement


This problem is from V.I Arnold's book Mathematics of Classical Mechanics.
Q) Show that every differential 1-form on line is differential of some function

Homework Equations


The differential of any function is
$$df_{x}(\psi): TM_{x} \rightarrow R$$

The Attempt at a Solution



The tangent to line is line itself. The differential 1-form is ##dy-dx=0##. Here I am struct. I don't know how to find out the differential. Can anyone help?
 

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Answers and Replies

  • #2
Orodruin
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The tangent to line is line itself.
No.

The differential 1-form is dy−dx=0dy−dx=0dy-dx=0.
No. A general differential 1-form is of the form ##\omega = g(x) dx##. You have to show that there exists a function ##G(x)## such that ##\omega = dG##.
 
  • #3
Abhishek11235
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No.


No. A general differential 1-form is of the form ##\omega = g(x) dx##. You have to show that there exists a function ##G(x)## such that ##\omega = dG##.

That means I have to integrate. Can you provide me solution?
 
  • #4
Orodruin
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Can you provide me solution?
That would violate the forum rules, which you would realize if you had bothered reading them.
 

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