Geodesic sphere
= Geodesic sphere
{title2=$S_r(p)=\{q:d_g(p,q)=r\}$}
A geodesic sphere is a level set of <Riemannian distance> from a point. For sufficiently small positive $r$, it is the <exponential map> image of the radius-$r$ tangent sphere, a smooth compact hypersurface. The <Gauss lemma> makes its tangent space orthogonal to the radial direction. Larger distance spheres need not be smooth at the <cut locus>.