Sebasti\'an Mu\~noz Thon, Purdue
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PDL C-038
In a semi-Riemannian manifold, given a point and direction
on the boundary, we follow the geodesic flow until we hit another
point on the boundary with a certain direction. This defines a map
called the scattering relation. The scattering rigidity problem asks
to what extent the scattering relation determines the metric on the
manifold. We will present a result for stationary metrics using the
timelike version of this map. The proof relies on a (symplectic)
reduction to the scattering rigidity problem for magnetic-potential
systems, that is, Riemannian manifolds endowed with a closed 2-form
(the magnetic part) and a smooth function (the potential).