- #1
weio
- 11
- 0
Hey,
when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field [tex] V [/tex], ie like this :-
[tex] [\bigtriangledown_a, \bigtriangledown_b] [/tex] = [tex] \bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a [/tex] = [tex] V;_a_b - V;_b_a [/tex]
But why does this difference of antisymmtery give us the Riemman tensor?
thanks
when calculating the Riemann curvature tensor, you need to calculate the commutator of some vector field [tex] V [/tex], ie like this :-
[tex] [\bigtriangledown_a, \bigtriangledown_b] [/tex] = [tex] \bigtriangledown_a\bigtriangledown_b - \bigtriangledown_b\bigtriangledown_a [/tex] = [tex] V;_a_b - V;_b_a [/tex]
But why does this difference of antisymmtery give us the Riemman tensor?
thanks