Surface divergence
= Surface divergence
{title2=$\nabla_s\cdot\mathbf v$}
The surface divergence of an ambient <vector field> is the tangential <trace> $\nabla_s\cdot\mathbf v=(\delta_{ij}-n_in_j)\partial_jv_i$. For a tangent <vector field> it is the intrinsic <divergence>. For $\mathbf v=\mathbf n$ it gives the sum of the two principal <curvatures>; a sphere with outward normal has $\nabla_s\cdot\mathbf n=2/a$.