Support theorem for the transverse ray transform of tensor fields of rank 2

Anuj Abhishek

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arXiv · 1804.03796

Support theorem for the transverse ray transform of tensor fields of rank 2

Anuj Abhishek

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Abstract

Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given a symmetric tensor field f of rank 2, we show that if the transverse ray transform of f vanishes over an appropriate open set of maximal geodesics of M , then the support of f vanishes on the points of M that lie on the union of the aforementioned open set of geodesics.

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BibTeX RIS

Anuj Abhishek. 2018-04-11. Support theorem for the transverse ray transform of tensor fields of rank 2. https://arxiv.org/abs/1804.03796

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