Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concerning the existence of Einstein and Ricci soliton metrics on
  solvable Lie groups   In this work we investigate solvable and nilpotent Lie groups with special
metrics. The metrics of interest are left-invariant Einstein and algebraic
Ricci soliton metrics. Our main result shows that the existence of a such a
metric is intrinsic to the underlying Lie algebra. More precisely, we show how
one may determine the existence of such a metric by analyzing algebraic
properties of the Lie algebra in question and infinitesimal deformations of any
initial metric.
  Our second main result concerns the isometry groups of such distinguished
metrics. Among the completely solvable unimodular Lie groups (this includes
nilpotent groups), if the Lie group admits such a metric, we show that the
isometry group of this special metric is maximal among all isometry groups of
left-invariant metrics. We finish with a similar result for locally
left-invariant metrics on compact nilmanifolds.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess