Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Injectivity of the Heisenberg X-ray Transform   We initiate the study of X-ray tomography on sub-Riemannian manifolds, for
which the Heisenberg group exhibits the simplest nontrivial example. With the
language of the group Fourier Transform, we prove an operator-valued
incarnation of the Fourier Slice Theorem, and apply this new tool to show that
a sufficiently regular function on the Heisenberg group is determined by its
line integrals over sub-Riemannian geodesics. We also consider the family of
taming metrics $g_\epsilon$ approximating the sub-Riemannian metric, and show
that the associated X-ray transform is injective for all $\epsilon>0$. This
result gives a concrete example of an injective X-ray transform in a geometry
with an abundance of conjugate points.

16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
9
The categories of this paper are: nlin