Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiply-warped product metrics and reduction of Einstein equations   It is shown that for every multidimensional metric in the multiply warped
product form $\bar{M} = K\times_{f_1} M_1\times_{f_2}M_2$ with warp functions
$f_1$, $f_2$, associated to the submanifolds $M_1$, $M_2$ of dimensions $n_1$,
$n_2$ respectively, one can find the corresponding Einstein equations
$\bar{G}_{AB}=-\bar{\Lambda}\bar{g}_{AB}$, with cosmological constant
$\bar{\Lambda}$, which are reducible to the Einstein equations $G_{\alpha\beta}
= -\Lambda_1 g_{\alpha\beta}$ and $G_{ij} =-\Lambda_2 h_{ij}$ on the
submanifolds $M_1$, $M_2$, with cosmological constants ${\Lambda_1}$ and
${\Lambda_2}$, respectively, where $\bar{\Lambda}$, ${\Lambda_1}$ and
${\Lambda_2}$ are functions of ${f_1}$, ${f_2}$ and $n_1$, $n_2$.

21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph