Search results for "X-ray transforms"

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The X-Ray Transform for Connections in Negative Curvature

2016

We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of the attenuated ray transform on tensor fields with values in a Hermitian bundle (i.e. vector valued case). We also show that a connection and Higgs field on a Hermitian bundle are determined up to gauge by the knowledge of the parallel transport between boundary points along all possible geodesics. The main tools are an energy identity, the Pestov identity with a unitary connect…

Mathematics - Differential GeometryPure mathematicsHermitian bundlesGeodesic[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Connection (vector bundle)Boundary (topology)Dynamical Systems (math.DS)X-ray transforms01 natural sciencesinversio-ongelmatHiggs fieldsTensor fieldMathematics - Analysis of PDEsFOS: MathematicsSectional curvatureMathematics - Dynamical Systems0101 mathematicsmath.APMathematical PhysicsPhysicsX-ray transformParallel transport010102 general mathematicsStatistical and Nonlinear Physicsconnections010101 applied mathematicsHiggs fieldmath.DGDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Mathematics::Differential Geometrymath.DSAnalysis of PDEs (math.AP)[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]Communications in Mathematical Physics
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