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: Obtaining the connection from Parallel Transport

  1. Oct 11, 2008 #1
    How do I obtain the Levi-Civita connection from the concept of parallel transport?

    So Do Carmo asks to prove that for vector fields X, Y on M, and for c(t) an integral curve of X, i.e. c(t_0) = p and X(c(t)) = dc/dt, the covariant derivative of Y along X is the derivative of the parallel transport of Y(c(t)).

    Do I just prove that the derivative of the parallel transport of a vector field satisfies the definition of an affine connection, metric compatibility and symmetric properties?

    I tried doing this but I ran into some road blocks.

    Is there an elegant way prove this?
  2. jcsd
  3. Oct 11, 2008 #2
    I think I solved it. Thanks anyway.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook