Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of Left Invariant Riemannian metrics on Complex
  hyperbolic space   It is well known that $\mathbb{C}H^n$ has the structure of solvable Lie group
with left invariant metric of constant holomorphic sectional curvature. In this
paper we give the full classification of all possible left invariant Riemannian
metrics on this Lie group. We prove that all of these metrics are of constant
negative scalar curvature and only one of them is Einstein (up to isometry and
scaling). Finally, we present the relation between Ricci solitons on Heisenberg
group and Einstein metric on $\mathbb{C}H^n$.

6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat