1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Manifold bases

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data
    I am trying to show that
    [tex] \vec{e'}_a = \frac{\partial x^b}{\partial x'^a} \vec{e}_b [/tex]

    where the e's are bases on a manifold and the primes mean a change of coordinates
    I can get that [tex] \frac{\partial x^a}{ \partial x'^b} dx'^b \vec{e}_a = dx'^a \vec{e'}_a [/tex] from the invariance of ds but what should I do next?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 4, 2007 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You're dealing with coodinates bases, or else your expression above isn't true. Thus

    [tex]\vec{e}_b = \frac{\partial}{\partial x^b}[/tex]

    [tex]\vec{e'}_a = \frac{\partial}{\partial x'^a}.[/tex]
  4. Oct 6, 2007 #3
    Yes, I am dealing with coordinate bases.

    How can you set a basis vector equal to a partial derivative operator?
    Last edited: Oct 6, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Manifold bases
  1. Pull Back on Manifolds (Replies: 0)

  2. Bragg peaks and bases (Replies: 1)

  3. Metric in Manifold (Replies: 0)