In this paper we find many families in the product space a??2?—a?? of complete embedded, simply connected, minimal and surfaces with constant mean curvature H such that |H|a‰¤1/2. We study complete surfaces invariant either by parabolic or by hyperbolic screw motions. We study the notion of isometric associate immersions. We exhibit an explicit formula for a Scherk-type minimal surface. We give a one-parameter family of entire vertical graphs of mean curvature 1/2. We prove a generalized Bour lemma that can be applied to a??2?—a??,e???2?—a?? and to Heisenberga€?s space to produce a family of screw motion surfaces isometric to a given one.
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