A characterization of tori with constant mean curvature in space form

  • Renato de Azevedo Tribuzy
Article

Keywords

Fundamental Form Space Form Constant Curvature Isometric Immersion Symmetric Bilinear Form 
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References

  1. [1]
    Alfors, L. and Sario, L.,Riemann Surfaces, Princeton University Press, Princeton (1960).Google Scholar
  2. [2]
    Chern, S. S.,An elementary proof of the existence of isothermal parameters on a surface, Proc. Amer. Math. Soc., 6 (1955), 771–782.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Chern, S. S. and Goldberg S. I.,On the volume decreasing property of a class of real harmonic mappings, Amer. J. Math., vol. 97, no 1, (1975) 133–147.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Hoffman, D. A.,Surfaces of constant mean curvature in manifolds of Constant Curvature, J. Differential Geometry, 8 (1973) 161–176.MATHMathSciNetGoogle Scholar
  5. [5]
    Hopf, H.,Lectures on differential geometry in the Large, Stanford University (1956).Google Scholar
  6. [6]
    Huber, A.,On subharmonic functions and differential geometry in the Large, Comment. Math. Helv. 32 (1957) 13–72.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Klotz, T. and Osserman, R.,Complete surfaces in E 3 with constant mean curvature, Comment. Math. Helv. 41 (1966–67), 313–318.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Lawson, H. B. Jr.,Complete Minimal Surfaces in S 3, Ann. of Math. 92 (1970).Google Scholar
  9. [9]
    Scherrer, W.,Die Grundgleichungen der Flächen theorie II, Comment. Math. Helv 32 (1957), 73–84.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Spivak, M.,A comprehensive introduction to differential geometry, Publish on Porish, Inc. Boston, Mass. Vol I–V (1970–1975).Google Scholar
  11. [11]
    Tribuzy, R. A.,Hopf's Method and Deformations of Surfaces Preserving Mean Curvature, An. Acad. Bras. Ciênc., (1978) 50 (4).Google Scholar
  12. [12]
    Yau, S.,Submanifolds with constant mean curvature I, Amer. J. Math., 96 (1974) 346–366.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Sociedade Brasileira de Matemática 1980

Authors and Affiliations

  • Renato de Azevedo Tribuzy
    • 1
  1. 1.Departamento de Matemática-ICEUniversidade do AmazonasManausBrasil

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