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arXiv · 1701.01972

Zero $f$-mean curvature surfaces of revolution in the Lorentzian product $\Bbb G^2\times\Bbb R_1$

Doan The Hieu·Tran Le Nam
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Abstract

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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Doan The Hieu, Tran Le Nam. 2017-01-08. Zero $f$-mean curvature surfaces of revolution in the Lorentzian product $\Bbb G^2\times\Bbb R_1$. https://arxiv.org/abs/1701.01972

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