# Only conservative vector fields are path independent?

1. Aug 4, 2014

### princejan7

does anyone have a proof of this?

2. Aug 4, 2014

### micromass

Could you elaborate on your statement? What does it mean for a vector field to be path independent? Could you give the precise statement (which I guess have to do something with integrals over a path). Furthermore, in what generality are you interested? Manifolds, surfaces in $\mathbb{R}^n$, open subsets of $\mathbb{R}^2$?

3. Aug 14, 2014