# Covariant differentiation on 2-sphere

1. May 22, 2013

### felixphysics

Consider a 2-sphere S2 with coordinates xμ=(θ,$\phi$) and metric ds2=dθ2+sin2θ d$\phi$2 and a vector $\vec{V}$ with components Vμ=(0,1). Calculate the following quantities.

θ$\phi$Vθ

$\phi$θVθ

2. May 22, 2013

### Mandelbroth

[Mods should move this to calculus and beyond, methinks.]

I believe the formula for this case would be $\nabla_{i}\mathbb{e}_j = \left\{\begin{array}\\{ij}\\{k}\end{array}\right\}\mathbb{e}_k$. However, you've shown no work, so I can't help you.