JMAT_V1_N2_A1 Talat Körpinar Essin Turhan Journal on Mathematics 2277-5137 1 2 1 6 Biharmonic curve, Heisenberg group, Sabban frame In this paper, we study surfaces according to Sabban frame in the Heisenberg group Heis . We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of biharmonic curves are helices in the Heisenberg group Heis . Finally, we find explicit parametric equations of surfaces according to Sabban Frame. April - June 2012 Copyright © 2012 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=1844