\partialμgλρ - \partialρgμλ = 0
I have reaced to this statement. Is this true? How?
What I thought is it looks like field strength tensor, but symmetric hence we can say it is true.
Thank you.
Consider a 2-sphere S2 with coordinates xμ=(θ,\phi) and metric ds2=dθ2+sin2θ d\phi2 and a vector \vec{V} with components Vμ=(0,1). Calculate the following quantities.
∇θ∇\phiVθ
∇\phi∇θVθ