= Affine exponential map
{title2=$\exp_p(X)=\gamma_X(1)$}
For an <affine connection>, let $\gamma_X$ be the affinely parametrized <geodesic> starting at $p$ with velocity $X$. Define the exponential map by the displayed formula for initial velocities whose <geodesics> exist until parameter one. It is defined near zero, has differential equal to the identity there, and obeys $\exp_p(tX)=\gamma_X(t)$ wherever defined. This construction requires no metric and extends the metric <exponential map>.
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