Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Curvilinear coordinates on tangent spaces

  1. Dec 7, 2013 #1
    Hello,

    if we consider a diffeomorphism f:M-->N between two manifolds, we can easily obtain a basis for the tangent space of N at p from the differential of f.

    I was wondering, why should we always express tangent vectors as linear combinations of tangent basis vectors?

    Could it be useful in some circumstances to express tangent vectors in some convenient system of curvilinear coordinates?

    If so, then could we interpret the introduction of local curvilinear coordinates as a diffeomorphism of the tangent space?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Curvilinear coordinates on tangent spaces
Loading...