= Geodesic X-ray transform
{title2=$I_g\beta(\gamma)=\int\beta_{\gamma(t)}(\dot\gamma(t),\dot\gamma(t))\,dt$}
For a symmetric covariant two-tensor, the geodesic transform integrates its evaluation on the unit velocity along boundary-to-boundary or closed <geodesics>, as appropriate to the manifold. A <potential symmetric 2-tensor> gives a total derivative along each geodesic and therefore integrates to zero on closed geodesics; boundary data require the corresponding boundary potential to vanish.
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