Title: Surfaces as Graphs of Finite Type in H2 × R
Author(s): Ahmed Azzi, Zoubir Hanifi, Mohammed Bekkar
Pages: 838-848
Cite as:
Ahmed Azzi, Zoubir Hanifi, Mohammed Bekkar, Surfaces as Graphs of Finite Type in H2 × R, Int. J. Anal. Appl., 18 (5) (2020), 838-848.


In this paper, we prove that ∆X = 2H where ∆ is the Laplacian operator, r = (x, y, z) the position vector field and H is the mean curvature vector field of a surface S in H2 × R and we study surfaces as graphs in H2 × R which has finite type immersion.

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  1. M. Bekkar, B. Senoussi, Translation surfaces in the 3-dimensional space satisfying ∆III ri = µiri, J. Geom. 103 (2012), 367-374. Google Scholar

  2. M. Bekkar, H, Zoubir, Surfaces of revolution in the 3-dimensional Lorentz Minkowski space satisfying ∆j ri = µiri, Int. J. Contemp. Math. Sci. 3 (2008), 1173-1185. Google Scholar

  3. B-Y. Chen, Total mean curvature and submanifolds of finite type, (2nd edition), World Scientific Publisher, Singapore, 1984. Google Scholar

  4. F. Dillen, L. Verstraelen, G. Zafindratafa, A generalization of the translation surfaces of Scherk. Differential Geometry in Honor of Radu Rosca: Meeting on Pure and Applied Differential Geometry, Leuven, Belgium, 1989, KU Leuven, Departement Wiskunde (1991), pp. 107–109. Google Scholar

  5. D. Hoffman, H. Matisse, The computer-aided discovery of new embedded minimal surfaces, Math. Intell. 9 (1987) 8–21. Google Scholar

  6. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401–487. Google Scholar

  7. B. Senoussi, M. Bekkar, Translation surfaces of finite type in H3 and Sol3, Anal. Univ. Orad. Fasc. Math. Tom, XXVI (1) (2019), 17-29. Google Scholar

  8. D.W. Yoon, On Translation surfaces with zero Gaussian curvature in H2 ×R, Int. J. Pure Appl. Math. 99 (3) 2015, 289-297. Google Scholar

  9. D.W. Yoon, Coordinate finite type invariante surfaces in Sol spaces, Bull. Iran. Math. Soc. 43 (2017), 649-658. Google Scholar


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