Original scientific paper

https://doi.org/10.21857/yk3jwhnl19

Null-translation surfaces with constant curvatures in Lorentz-Minkowski 3-space

Ivana Filipan orcid.org/0000-0001-6616-3206 ; Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, 10 000 Zagreb, Croatia
Željka Milin Šipuš orcid.org/0000-0002-0726-3335 ; Faculty of Science, Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
Ljiljana Primorac Gajčić orcid.org/0000-0002-8460-3196 ; Department of Mathematics, University J. J. Strossmayer of Osijek, 31 000 Osijek, Croatia

Abstract

Translation surface is a surface formed by two curves moving along each other. In this paper we analyze this kind of surfaces in Lorentz-Minkowski 3-space R13, which is the smooth manifold R3 endowed by a flat Lorentzian pseudometric. Translation surfaces in R13 can be classified with respect to the causal character of their generating curves (spacelike, timelike or null (lightlike)). We are specially interested in translation surfaces generated by at least one null curve, which we refer to as null-translation surfaces. In the present paper we determine all nulltranslation surfaces of constant mean curvature and prove that the only null-translation surfaces of constant Gaussian curvature are cylindrical surfaces.

Keywords

Translation surface; null curve; mean curvature; Gaussian curvature

Hrčak ID:

307498

URI

https://hrcak.srce.hr/307498

Publication date:

25.8.2023.

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