Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities of Connection Ricci Flow and Ricci Harmonic Flow   In this paper, we study the singularities of two extended Ricci flow systems
--- connection Ricci flow and Ricci harmonic flow using newly-defined curvature
quantities. Specifically, we give the definition of three types of
singularities and their corresponding singularity models, and then prove the
convergence. In addition, for Ricci harmonic flow, we use the monotonicity of
functional $\nu_\alpha$ to show the connection between finite-time singularity
and shrinking Ricci harmonic soliton. At last, we explore the property of
ancient solutions for Ricci harmonic flow.

23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph