Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero $f$-mean curvature surfaces of revolution in the Lorentzian product
  $\Bbb G^2\times\Bbb R_1$   We classify (spacelike or timelike) surfaces of revolution with zero $f$-mean
curvature in $\Bbb G^2\times\Bbb R_1,$ the Lorentz-Minkowski 3-space $\Bbb
R^3_1$ endowed with the Gaussian-Euclidean density $e^{-f(x,y,z)}=\frac
1{2\pi}e^{-\frac{x^2+y^2}2}.$ It is proved that an $f$-maximal surface of
revolution is either a horizontal plane or a spacelike $f$-Catenoid. For the
timelike case, a timelike $f$-minimal surface is either a vertical plane
containing $z$-axis, the cylinder $x^2+y^2=1,$ or a timelike $f$-Catenoid.
Spacelike and timelike $f$-Catenoids are new examples of $f$-minimal surfaces
in $\Bbb G^2\times \Bbb R_1.$

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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: physics
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int