1. The problem statement, all variables and given/known data I am trying to derive the line element for this geometry. But I am not sure how to show that ds cant contain any crossterms of [itex]d\theta [/itex] and [itex] d\phi [/itex] 2. Relevant equations ds must be invariant under reflections [itex]\theta \rightarrow \theta'=\pi - \theta [/itex] and [itex]\phi \rightarrow \phi' = -\phi [/itex] 3. The attempt at a solution Well I just put in this in the equation for the line element. assuming t=r=konstant. [itex]ds^2=Ad\theta^2 + Bd\phi^2 + Cd\theta d\phi [/itex] and the line element after reflection: [itex]ds^2=Ad\theta^2 + Bd\phi^2 + Cd\theta d\phi [/itex] Ah, and for a 2 sphere [itex]A=R^2[/itex] and [itex]B=R^2sin^2\theta[/itex] How can I show that C=0?