CMC and CGC surfaces in Lorentz Heisenberg group H3

Bensikaddour, Djemaia

doi:10.47974/JIM-1532

Open Access Research Article

CMC and CGC surfaces in Lorentz Heisenberg group H3

^*Djemaia BensikaddourCorresponding authormd.bensikaddour@gmail.comDepartment of Mathematics and Computer ScienceUniversity of MostaganemMostaganem, BP 227, 27000, AlgeriaView full profile →

* Corresponding author · click or hover a name for details

pp. 937–950Vol. 26Issue 5August 2023DOI: 10.47974/JIM-1532XML

Received:: 05 Jan 2022
Accepted:: 12 Jul 2022
Published Online:: 08 Sep 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1532
Pages:: 937–950

Abstract

The aim of this paper is to study the characterization of some constant mean curvature (CMC) and constant Gauss curvature (CGC) A-net surfaces in the 3-dimensional Lorentz-Heisenberg group H3 endowed with a left invariant Lorentzian metric gi in the three following cases : 1. g1 = -dx2 + dy2 + (xdy + dz)2, 2. g2 = dx2 + dy2 - (xdy + dz)2. 3. g3 = dx2 + (xdy + dz)2 - [(1 - x)dy - dz]2. Using Levi-Civita connection, we will calculate the mean curvature H and the Gaussian curvature K in order to study CMC and CGC A-net surfaces in (H3, g1), (H3, g2) and (H3, g3).

Keywords

Constant mean curvature Gaussian curvature Surface A-net surface Lorentz-Heisenberg group

Subject Classifications

(2010) 53A1053C3053C42

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