Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Functions of constant geodesic X-ray transform   We show that the existence of a function in $L^{1}$ with constant geodesic
X-ray transform imposes geometrical restrictions on the manifold. The boundary
of the manifold has to be umbilical and in the case of a strictly convex
Euclidean domain, it must be a ball. Functions with constant geodesic X-ray
transform always exist on manifolds with rotational symmetry.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex