CMC and CGC surfaces in Lorentz Heisenberg group H3

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).