30 citations · 73 across the 24 of their papers we have counts for
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math.DG2018
Functions of constant geodesic X-ray transform
Joonas Ilmavirta, Gabriel P. Paternain
We show that the existence of a function in with constant geodesic X-ray transform imposes geometrical restrictions on the manifold. The boundary of the manifold has to be…
math.DG2018
Broken ray tensor tomography with one reflecting obstacle
Joonas Ilmavirta, Gabriel P. Paternain
We show that a tensor field of any rank integrates to zero over all broken rays if and only if it is a symmetrized covariant derivative of a lower order tensor which satisfies a sy…
math.DG2018
Convex projective surfaces with compatible Weyl connection are hyperbolic
Thomas Mettler, Gabriel P. Paternain
We show that a properly convex projective structure on a closed oriented surface of negative Euler characteristic arises from a Weyl connection if and only if $\math…