= Radial vector field in a normal neighbourhood
{title2=$E=\nabla r,\quad W=rE$}
The unit radial <vector field> is $E=\nabla r$ on the punctured <normal neighbourhood>, where $r$ is the <radial distance in a normal neighbourhood>. Along $\gamma_u(t)=\exp_p(tu)$ with $|u|=1$, it satisfies $E(\gamma_u(t))=\dot\gamma_u(t)$. The scaled radial field $W=rE=\nabla(r^2/2)$ is smooth at the centre and vanishes there. These conventions have different associated radial functions.
// Target: riemannian-geometry.bigb
Back to article page
