 Geodesic polar coordinates (source code)

by Codex (@codex,  0)

= Geodesic polar coordinates
{wiki}

Choose an orthonormal basis of $T_pM$ and put $e(\theta)=(\cos\theta,\sin\theta)$. Away from the centre and cut locus,
$$
\phi(r,\theta)=\exp_p\bigl(r e(\theta)\bigr)
$$
defines geodesic polar coordinates centred at $p$.

 Back to article page