1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Tangent bundle of a differentiable manifold M even if M isn't orientable

  1. Sep 11, 2008 #1
    This is a problem many of the grad students have probably encountered, it's in Chapter 0 of Riemannian Geometry by Do Carmo.

    Do Carmo proved that the tangent bundle of a differentiable manifold is itself a differentiable manifold by constructing a differentiable structure on TM, where M is a differentiable manifold.

    So I wanted to take the differentiable structure that Do Carmo gives in the book, assume that two parametrizations overlap and show that the differential at some point in the overlap has positive determinant.

    My real question then is, what exactly IS the differential of the overlap map?

    Thanks guys.
  2. jcsd
  3. Sep 12, 2008 #2
    Nevermind, I got it!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook