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Translation hypersurfaces with constant scalar curvature into the Euclidean space

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Abstract

In this paper, a complete description of all translation hypersurfaces with constant scalar curvature in the Euclidean space is presented.

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References

  1. H. Alencar, W. Santos and D. Zhou, Stable hypersurfaces with constant scalar curvature curvature, Proceding of the American Mathematical Society 138 (2010), 3301–3312.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Caminha, On spacelike hypersurfaces of constant sectional curvature lorentz manifolds, Journal of Geometry and Physics 56 (2006), 1144–1174.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Chen, H. Sun and L. Tang, On translation Hypersurfaces with constant mean curvature in (n+1)-dimensional spaces, Journal of Beijing Institute of Technology 12 (2003), 322–325.

    MathSciNet  MATH  Google Scholar 

  4. F. Dillen, L. Verstraelen and G. Zafindratafa, A generalization of the translational surfaces of Scherk, in Differential Geometry in honor of Radu Rosca, Catholic University of Leuven-Belgium, 1991, pp. 107–109.

  5. M. L. Leite, An example of a triply periodic complete embedded scalr-flat hypersurface of ℝ4, Anais da Academia Brasileira de Cincias 63 (1991), 383–385.

    MathSciNet  Google Scholar 

  6. H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, Journal of Geometry 64 (1999), 141–149.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. López, Minimal translation surfaces in hyperbolic space, Beiträge zur Algebra und Geometrie 52 (2011), 105–112.

    Article  MATH  Google Scholar 

  8. T. Okayasu, O(2)×O(2)-invariant hypersurfaces with constant negative scalar curvature in ℝ4, Proceeding of the American Mathematical Society 107 (1989), 1045–1050.

    MathSciNet  MATH  Google Scholar 

  9. T. Okayasu, New examples of complet hypersurfaces with constant positive scalar curvature in the Euclidean space, Journal of the Mathematical Society of Japan 62(4) (2010), 1137–1166.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Reilly, On the Hessian of a function and the curvatures of its graph, The Michigan Mathematical Journal 20 (1973), 373–383.

    MathSciNet  MATH  Google Scholar 

  11. H. F. Scherk, Bemerkungenüber die kleinste Fläche innerhalb gegebener Grenzen, Journal für die reine und angewandte Mathematik 13 (1835), 185–208.

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Piauí, 64049-550, Ininga - Teresina - PI, Brazil

    Barnabé Pessoa Lima, Newton Luís Santos & Paulo Alexandre Araújo Sousa

Authors
  1. Barnabé Pessoa Lima
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  2. Newton Luís Santos
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  3. Paulo Alexandre Araújo Sousa
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Corresponding author

Correspondence to Barnabé Pessoa Lima.

Additional information

Partially supported by PROCAD/CAPES, Brazil.

Partially supported by PROCAD/CAPES, Brazil.

Partially supported by CNPq and PROCAD/CAPES, Brazil.

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Lima, B.P., Santos, N.L. & Sousa, P.A.A. Translation hypersurfaces with constant scalar curvature into the Euclidean space. Isr. J. Math. 201, 797–811 (2014). https://doi.org/10.1007/s11856-014-1083-2

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  • DOI: https://doi.org/10.1007/s11856-014-1083-2

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