  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.

Differential Geometry