# Homework Help: Spin connection

1. Sep 15, 2014

### m1rohit

1. The problem statement, all variables and given/known data

I want to know wether the component [itex]\omega_{c}^{ab}[itex] of the spin connection is zero or not?

2. Relevant equations
[itex]de^{a}=-\omega^{a}_{b}\wedge e^{b}[itex]

3. The attempt at a solution
[itex]de^{a}=-\omega^{a}_{b}\wedge e^{b}[itex]
$=-\omega^{a}_{b,\nu} e^{b}_{\mu} dx^{\nu}\wedge dx^{\mu}$
$=-\omega^{a}_{b,c} e^{b}_{[\mu}e^{c}_{\nu]} dx^{\nu}\wedge dx^{\mu}$
as it is antisymmetric in $\mu$ and $\nu$.So it is also antisymmetric in b and c.Thus one can conclude from here.

Last edited: Sep 15, 2014
2. Sep 15, 2014

### nrqed

I have reformatted your question so that the TeX commands would be visible.