Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncompact homogeneous Einstein manifolds attached to graded Lie
  algebras   In this paper, we study the nilradicals of parabolic subalgebras of
semisimple Lie algebras and the natural one-dimensional solvable extensions of
them. We investigate the structures, curvatures and Einstein conditions of the
associated nilmanifolds and solvmanifolds. We show that our solvmanifold is
Einstein if the nilradical is of two-step. New examples of Einstein
solvmanifolds with three-step and four-step nilradicals are also given.

4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics