A support theorem for the geodesic ray transform of symmetric tensor fields

2008/03/20 by Krishnan, Venky, Stefanov, Plamen · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0803.3062

Abstract

Let (M,g) be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of f along maximal geodesics vanish on an appropriate open subset of the space of geodesics in M. Under the assumption that the metric g is real-analytic, it is shown that there exists a vector field v satisfying f=dv on the set of points lying on these geodesics and v=0 on the intersection of this set with the boundary \PD M of the manifold M. Using this result, a Helgason's type of a support theorem for the geodesic ray transform is proven. The approach is based on analytic microlocal techniques.

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• Reconstruction of scalar functions and vector fields from weighted V-line transforms with swinging branches
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