Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classical N-body problem in the context of curved space   We provide the differential equations that generalize the Newtonian N-body
problem of celestial mechanics to spaces of constant Gaussian curvature, k, for
all k real. In previous studies, the equations of motion made sense only for k
nonzero. The system derived here does more than just include the Euclidean case
in the limit when k tends to 0: it recovers the classical equations for k=0.
This new expression of the laws of motion allows the study of the N-body
problem in the context of constant curvature spaces and thus offers a natural
generalization of the Newtonian equations that includes the classical case. We
end the paper with remarks about the bifurcations of the first integrals.

27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga