2020/09/28 by Chen, Dong, Erchenko, Alena, Gogolev, Andrey
#37D40 (primary) 37D20 #53C21 (secondary) #53C24 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2009.13665
Let Σ be a Riemannian manifold with strictly convex spherical boundary. Assuming absence of conjugate points and that the trapped set is hyperbolic, we show that Σ can be isometrically embedded into a closed Riemannian manifold with Anosov geodesic flow. We use this embedding to provide a direct link between the classical Livshits theorem for Anosov flows and the Livshits theorem for the X-ray transform which appears in the boundary rigidity program. Also, we give an application for lens rigidity in a conformal class.