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

Torsion Tensor in Terms of Metric Tensor

  1. Jul 10, 2015 #1
    Would it be possible to write the torsion tensor in terms of the metric? I know that a symmetric Christoffel Symbol can be written in terms of the partial derivatives of the metric. This definition of the christoffel symbols does not apply if they are not symmetric. Is it possible to write a definition of the non-symmetric christoffel symbols in terms of a metric, and from that find an equation for the torsion tensor, or is it independent of the metric tensor?
  2. jcsd
  3. Jul 10, 2015 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    The torsion free condition is required to uniquely define a metric compatible connection. If you let it go, there are several possible metrics (one of which is the torsion free one).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook