Constant mean curvature surfaces in 4 -space forms

Jost-Hinrich Eschenburg; Renato de Azevedo Tribuzy

Rendiconti del Seminario Matematico della Università di Padova (1988)

  • Volume: 79, page 185-202
  • ISSN: 0041-8994

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Eschenburg, Jost-Hinrich, and Tribuzy, Renato de Azevedo. "Constant mean curvature surfaces in $4$-space forms." Rendiconti del Seminario Matematico della Università di Padova 79 (1988): 185-202. <http://eudml.org/doc/108094>.

@article{Eschenburg1988,
author = {Eschenburg, Jost-Hinrich, Tribuzy, Renato de Azevedo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {isothermal coordinates; isometric immersions; Riemannian surface; parallel mean curvature vector},
language = {eng},
pages = {185-202},
publisher = {Seminario Matematico of the University of Padua},
title = {Constant mean curvature surfaces in $4$-space forms},
url = {http://eudml.org/doc/108094},
volume = {79},
year = {1988},
}

TY - JOUR
AU - Eschenburg, Jost-Hinrich
AU - Tribuzy, Renato de Azevedo
TI - Constant mean curvature surfaces in $4$-space forms
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1988
PB - Seminario Matematico of the University of Padua
VL - 79
SP - 185
EP - 202
LA - eng
KW - isothermal coordinates; isometric immersions; Riemannian surface; parallel mean curvature vector
UR - http://eudml.org/doc/108094
ER -

References

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  1. [1] F.J. Almgren, Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem, Ann. of Math., 84 (1966), pp. 277-292. Zbl0146.11905MR200816
  2. [2] W. Blaschke, Einführung in die Differentialgeometrie, Springer (1950). Zbl0041.28804MR43502
  3. [3] R.L. Bryant, Conformal and minimal immersions of compact surfaces into the 4-sphere, J. Diff. Geom., 17 (1982), pp. 455-473. Zbl0498.53046MR679067
  4. [4] E. Calabi, Minimal immersions of surfaces in Euclidean spheres, J. Diff. Geom., 1 (1967), pp. 111-125. Zbl0171.20504MR233294
  5. [5] S.S. Chern, On the minimal immersions of the two-sphere in a space of constant curvature, Problems in Analysis, ed. Gunning, Princeton, N. J. (1970), pp. 27-40. Zbl0217.47601MR362151
  6. [6] S.S. Chern, On surfaces of constant mean curvature in a three-dimensional space of constant curvature, Geometric Dynamics, Springer L.N. in Mathematics, 1007 (1981), pp. 104-108. Zbl0521.53006MR730266
  7. [7] J.H. Eschenburg - I.V. Guadalupe - R. Tribuzy, The fundamental equations of minimal surfaces in CP2, Math. Ann., 270 (1985), pp. 571-598. Zbl0536.53056MR776173
  8. [8] I.V. Guadalupe - C. Gutierrez - J. Sotomayor - R. Tribuzy, Principal lines on surfaces minimally immersed in constantly curved 4-spaces, Preprint IMPA (1985). Zbl0633.53010
  9. [9] H. Hopf, Differential geometry in the large (Stanford lectures, 1956), Springer L.N. in Mathematics, 1000 (1983). Zbl0526.53002MR707850
  10. [10] G.R. Jensen - M. RIGOLI, Minimal surfaces in spheres by the method of moving frames, PreprintUniversité de Nancy I (1983). Zbl0706.53008
  11. [11] R. Lashof - S. SMALE, On the immersion of manifolds in Euclidean space, Ann. of Math., 68 (1959), pp. 562-583. Zbl0097.38805MR103478
  12. [12] B. Lawson, Complete minimal surfaces in S3, Ann. of Math., 92 (1970), pp. 335-374. Zbl0205.52001MR270280
  13. [13] L. Rodriguez - I. V. GUADALUPE, Normal curvature of surfaces in space forms, Pacific J. of Math., 106 (1983), pp. 95-106. Zbl0515.53044MR694674
  14. [14] E.A. Ruh, Minimal immersions of the 2-sphere in S4, Proc. Am. Math. Soc., 28 (1971), pp. 218-222. Zbl0212.54003MR271880
  15. [15] M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. IV, Publish or Perish (1975). Zbl0306.53001MR394452
  16. [16] R. Tribuzy - I. V. GUADALUPE, Minimal immersions of surfaces into 4-dimensional space forms, Rend. Sem. Mat. Univ. Padova, 73 (1985), pp. 1-13. Zbl0573.53036MR799891
  17. [17] S.T. Yau, Submanifolds with constant mean curvature, I, Am. J. of Math., 96 (1974), pp. 346-366. Zbl0304.53041MR370443

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