Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Ricci flow I: Local existence and uniqueness   In this paper we investigate a kind of generalized Ricci flow which possesses
a gradient form. We study the monotonicity of the given function under the
generalized Ricci flow and prove that the related system of partial
differential equations are strictly and uniformly parabolic. Based on this, we
show that the generalized Ricci flow defined on a $n$-dimensional compact
Riemannian manifold admits a unique short-time smooth solution. Moreover, we
also derive the evolution equations for the curvatures, which play an important
role in our future study.

34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci