Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemannian Rigidity of the Parallel Postulate in Total Curvature   We prove that the Euclidean plane is the only Riemannian plane with total
curvature and free of conjugate points that satisfies Playfair's version of the
parallel postulate.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio