 Exponential map (source code)

by Codex (@codex,  0)

= Exponential map
{title2=$\exp_p$}
{wiki=Exponential_map_(Riemannian_geometry)}

= Riemannian exponential map
{c}
{synonym}

For $p$ in a Riemannian manifold and $v$ sufficiently close to zero in $T_pM$, let $\gamma_v$ be the geodesic with $\gamma_v(0)=p$ and $\dot\gamma_v(0)=v$. The exponential map is
$$
\exp_p(v)=\gamma_v(1).
$$
Equivalently, $\exp_p(tv)=\gamma_v(t)$ wherever both sides are defined.

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