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Translation surfaces in the three-dimensional simply isotropic space $𝕀_{3}^{1}$

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- Translation surfaces in the three-dimensional simply isotropic space $𝕀_{3}^{1}$

Murat Kemal Karacan

Department of Mathematics, Faculty of Sciences and Arts, Usak University, 1 Eylul Campus, 64200 Usak, Turkey

E-mail Address: murat.karacan@usak.edu.tr

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Dae Won Yoon

Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 660-701, South Korea

E-mail Address: dwyoon@gnu.ac.kr

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, and

Bahaddin Bukcu

Department of Mathematics, Faculty of Sciences and Arts, Gazi Osman Pasa University, 60250 Tokat, Turkey

E-mail Address: bbukcu@yahoo.com

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https://doi.org/10.1142/S0219887816500882Cited by:10 (Source: Crossref)

Abstract

In this paper, we classify translation surfaces in the three-dimensional simply isotropic space $𝕀_{3}^{1}$ under the condition $Δ^{i} x_{i} = λ_{i} x_{i}$ where $Δ$ is the Laplace operator with respect to the first and second fundamental forms and $λ$ is a real number. We also give explicit forms of these surfaces.

Keywords:

AMSC: 53A35, 53B30, 53A40

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