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A SUPPORT THEOREM FOR THE GEODESIC RAY TRANSFORM OF SYMMETRIC

By Tensor Fields, Venky Krishnan and Plamen Stefanov

Abstract

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 ∂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. 1

Topics: l(γ
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