2009/10/21 by Pilar Herreros, Herreros, Pilar, James Vargo +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C22
paper · pdf · doi:10.48550/arxiv.0910.4189
arxiv created 2009/10/21 · arxiv updated 2009/12/01
Consider a compact Riemannian manifold with boundary endowed with a magnetic field. A path taken by a particle of unit charge, mass, and energy is called a magnetic geodesic. It is shown that if everything is real-analytic, the topology, metric, and magnetic field are uniquely determined by the scattering relation of the magnetic geodesic flow, measured at the boundary. Conjugate points are allowed with minor restrictions. In exchange for the real-analytic assumption, prior results in boundary rigidity are greatly generalized.