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

Why there is a minus sign in the Killing's equation

  1. May 19, 2013 #1
    With the Levi-Civita connection, the Killing's equation is:

    I can't understand why there is a minus sign in front of the Christoffel symbols.

    We have that:
    and because of [itex]{\Gamma^{c}}_{ab}={\Gamma^{c}}_{ba}[/itex], it should be
    and not with a minus sign.
  2. jcsd
  3. May 19, 2013 #2

    For tesor in variant components

  4. May 19, 2013 #3
    Oops, right, [tex]\xi_a[/itex] has lower index i.e. it's a component of covector and its covariant derivative has a minus sign in front of the connection coefficients. Thnx!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook