Geodesic circle
= Geodesic circle
{title2=$S_r(p)=\{\exp_p(rv):|v|=1\}$}
For $r$ smaller than the normal-coordinate radius, the <geodesic circle> on a <Riemannian surface> consists of points at distance $r$ from $p$. The <exponential map> restricted to the radius-$r$ circle in $T_pS$ gives its smooth embedded parameterization. Outside the injectivity range a distance sphere need not be smooth.