NONLINEAR STUDIES - www.nonlinearstudies.com Vol. 24, No. 4, pp. 859-867, 2017 c ⃝ CSP - Cambridge, UK; I&S - Florida, USA, 2017 Minimal translation surfaces in Lorentz Heisenberg 3−Space Djemaia Bensikaddour 1 , Lakehal Belarbi 2 ⋆ 1,2 Department of Mathematics Laboratory of Pure and Applied Mathematics University of Mostaganem (UMAB) B.P.227,27000,Mostaganem, Algeria. E-mail: 1 bensikaddour@yahoo.fr, 2 lakehalbelarbi@gmail.com ⋆ Corresponding Author. E-mail: lakehalbelarbi@gmail.com Abstract. In this work we study three types of minimal translation surfaces in the 3− dimensional Lorentz Heisenberg space H 3 obtained as a product of two planar curves lying in planes, which are not orthogonal. 1 Introduction The study of minimal surfaces and translation surfaces in 3−dimensional geometric spaces is the main objects of many researches recently. In 1835 H.F.Scherk studied translation surfaces in E 3 defined as graph of the function z = f (x)+ g(y), and he proved that, besides the planes, the only minimal translation surfaces are the surfaces given by z(x, y)= 1 A ln | cos(Ax) cos(Ay) | = 1 A ln | cos(Ax)|− 1 A ln | cos(Ay)|, (1.1) where f (x) and g(y) are smooth functions on some interval of R and A ∈ R ∗ . It is show in ([19]) and ([20]) that modulo an automorphism of the Lie algebra of the Heisenberg group there exist three classes of invariant Lorentzian metrics on the Heisenberg group one of which is flat. D.W.Yoon, C.W.Lee and M.K.Karacan studied minimal translation surfaces in the 3- dimensional Heisenberg group H 3 see ([27]) and in ([8]) A. Ferrandez and P. Lucas classified in 3- dimensional Lorentz-Minkowski space L 3 minimal surfaces which verify the condition ΔH = λH where Δ is the 2010 Mathematics Subject Classification: 53A45. 53C20. Keywords: Lorentz Heisenberg 3−Space, Translation surfaces, Minimal surfaces, Mean curvature.