UC Santa Cruz

In the literature on X-ray transform and Transport Twistor (TT) space, blow-down maps describe the degeneracy of the TT space of an oriented Riemannian surface, while collapsing (yet separating) geodesics of the unit tangent bundle of that surface. In the literature [3], such maps have been constructed for simple surfaces of near-constant curvature (see Definition 1.1), showing that the interior of their TT space is biholomorphic to an open set in standard C 2 . The construction there relied on a microlocal argument leveraging the absence of conjugate points.In this dissertation, we construct explicit circularly symmetric examples, including examples with conjugate points, whose transport twistor spaces admit a global blow-down map.