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!

Lie group geometry

  1. Jul 29, 2006 #1
    I seem to be having difficulty proving something.
    I hope you can help me.

    I will write del_X(Y) when I refer to the levi-chivita connection (used on Y in the direction of X).

    Let G be a lie group, with a bi-invariant metric , g , on G.
    I want to prove that del_X(Y) = 0.5 [X,Y] (Lie brackets) , whenever X,Y are left-invariant vector fields on G.

    Thanks in advance.
  2. jcsd
  3. Aug 18, 2009 #2


    User Avatar

    The Levi-Civita connection can be expressed via the inner product (which is a fundamental result in metric differential geometry). Use this formula and bi-invariance to obtain the result.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Lie group geometry
  1. Lie Groups (Replies: 3)

  2. Lie Groups (Replies: 7)