English

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

Differential Geometry 2018-04-12 v1

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.

Keywords

Cite

@article{arxiv.1804.03796,
  title  = {Support theorem for the transverse ray transform of tensor fields of rank 2},
  author = {Anuj Abhishek},
  journal= {arXiv preprint arXiv:1804.03796},
  year   = {2018}
}