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Integral geometry of tensor fields on a class of non-simple Riemannian manifolds

Plamen Stefanov·Gunther Uhlmann
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Abstract

We study the geodesic X-ray transform $I_Γ$ of tensor fields on a compact Riemannian manifold $M$ with non-necessarily convex boundary and with possible conjugate points. We assume that $I_Γ$ is known for geodesics belonging to an open set $Γ$ with endpoint on the boundary. We prove generic s-injectivity and a stability estimate under some topological assumptions and under the condition that for any $(x,ξ)\in T^*M$, there is a geodesic without conjugate points in $Γ$ through $x$ normal to $ξ$.

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Plamen Stefanov, Gunther Uhlmann. 2006-11-16. Integral geometry of tensor fields on a class of non-simple Riemannian manifolds. https://arxiv.org/abs/math/0601178

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