Tohoku Mathematical Journal
2022
June
SECOND SERIES VOL. 74, NO. 2

Tohoku Math. J.
74 (2022), 263-286

Title CLASSIFICATION OF ZERO MEAN CURVATURE SURFACES OF SEPARABLE TYPE IN LORENTZ-MINKOWSKI SPACE

Author Seher Kaya and Rafael López

(Received July 20, 2020, revised January 18, 2021)
Abstract. Consider the Lorentz-Minkowski 3-space ${\mathbb L}^3$ with the metric $dx^2+dy^2-dz^2$ in canonical coordinates $(x,y,z)$. A surface in ${\mathbb L}^3$ is said to be separable if it satisfies an equation of the form $f(x)+g(y)+h(z)=0$ for some smooth functions $f$, $g$ and $h$ defined in open intervals of the real line. In this article we classify all zero mean curvature surfaces of separable type, providing a method of construction of examples.

Mathematics Subject Classification. Primary 53A10; Secondary 53C42.
Key words and phrases. Lorentz-Minkowski space, zero mean curvature, separable surface.

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