Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci Flow on Torus Bundles   In this paper we compute the Ricci flow formulas for invariant metrics on
prinicpal $G$-bundles compatible with the connection. Our primary focus is on
torus bundles which we use to study a notion of Bakry-\'Emery Ricci flow as
well as Ricci flow on circle bundles over K\"ahler-Einstein manifolds. The
latter application gives us solutions to Ricci flows on Heisenberg groups and
implicit solutions to Ricci flows on Berger 3-spheres and several other
3-dimensional manifolds.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys