Abstract
In this paper we study the relationship between the Laplace-Beltrami operator ∆ of the position vector field and the mean curvature vector field r of surfaces defined as a graph of functions in the three-dimensional Lorentzian Heisenberg group H_3^1 which is endowed with left invariant Lorentzian metrics g_i,( i=1,2,3) and we prove that the surface as graph is minimal in 〖 H〗_3^1, if and only if the components of the position vector field r are harmonic functions.
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