Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci flow for homogeneous compact models of the universe   Using quaternions, we give a concise derivation of the Ricci tensor for
homogeneous spaces with topology of the 3-dimensional sphere. We derive
explicit and numerical solutions for the Ricci flow PDE and discuss their
properties. In the collapse (or expansion) of these models, the interplay of
the various components of the Ricci tensor are studied. We dedicate this paper
to honor the work of Josh Goldberg.

1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat