Minimal immersions of surfaces into 4-dimensional space forms

Renato de Azevedo Tribuzy; Irwen Valle Guadalupe

Rendiconti del Seminario Matematico della Università di Padova (1985)

  • Volume: 73, page 1-13
  • ISSN: 0041-8994

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Tribuzy, Renato de Azevedo, and Valle Guadalupe, Irwen. "Minimal immersions of surfaces into 4-dimensional space forms." Rendiconti del Seminario Matematico della Università di Padova 73 (1985): 1-13. <http://eudml.org/doc/107978>.

@article{Tribuzy1985,
author = {Tribuzy, Renato de Azevedo, Valle Guadalupe, Irwen},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {normal curvature; minimal immersion; Veronese surface; Clifford torus},
language = {eng},
pages = {1-13},
publisher = {Seminario Matematico of the University of Padua},
title = {Minimal immersions of surfaces into 4-dimensional space forms},
url = {http://eudml.org/doc/107978},
volume = {73},
year = {1985},
}

TY - JOUR
AU - Tribuzy, Renato de Azevedo
AU - Valle Guadalupe, Irwen
TI - Minimal immersions of surfaces into 4-dimensional space forms
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1985
PB - Seminario Matematico of the University of Padua
VL - 73
SP - 1
EP - 13
LA - eng
KW - normal curvature; minimal immersion; Veronese surface; Clifford torus
UR - http://eudml.org/doc/107978
ER -

References

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  1. [1] L. Ahlfors - L. Sario, Riemann surfaces, Princeton University Press, Princeton, 1960. Zbl0196.33801MR114911
  2. [2] A.C. Asperti, Immersions of surfaces into 4-dimensional spaces with nonzero normal curvature, Ann. Mat. Pura Appl., 125 (1980), pp. 313-328. Zbl0453.53045MR605213
  3. [3] L.R. Bryant, Every compact Riemann surface may be immersed conformally and minimally into S4, preprint. 
  4. [4] E. Calabi, Minimal immersions of surfaces in euclidean spheres, J. Diff. Geometry, 1 (1967), pp. 111-125. Zbl0171.20504MR233294
  5. [5] M. Do Carmo - N. Wallach, Representation of compact groups and minimal immersions into spheres, J. Diff. Geometry, 4 (1970), pp. 91-104. Zbl0197.18301MR266104
  6. [6] B.Y. Chen, Geometry of submanifolds, New York, M. Dekker (1973). Zbl0262.53036MR353212
  7. [7] S.S. Chern, On minimal spheres in the four-sphere, in Studies and Essays, presented to Y. W. Chen, Taiwan (1970), pp. 137-150. Zbl0212.26402MR278205
  8. [8] S.S. Chern, On the minimal immersions of the two sphere in a space of constant curvature, Problems in Analysis, Princeton University Press (1970), pp. 27-40. Zbl0217.47601MR362151
  9. [9] S.S. Chern - R. Osserman, Remarks on the Riemannian metric of a minimal submanifold, preprint. Zbl0477.53056
  10. [10] T. Itoh, Minimal surfaces in 4-dimensional Riemannian manifolds of constant curvature, Kodai Math. Sem. Rep., 23 (1971), pp. 415-458. Zbl0249.53045MR317248
  11. [11] H.B. Lawsonjr., Complete minimal surfaces in S3, Ann. of Math., 92 (1970), pp. 335-374. Zbl0205.52001
  12. [12] H.B. Lawsonjr., Some intrinsic characterizations of minimal surfaces, J. d'Analyse Mathematique, 24 (1971), pp. 152-161. Zbl0251.53003MR284922
  13. [13] J.A. Little, On singularities of submanifolds of a higher dimensional Euclidean space, Ann. Mat. Pura Appl., 83 (1969), pp. 261-335. Zbl0187.18903MR271970
  14. [14] C.L.E. Moore - E.B. Wilson, Differential geometry of two-dimensional surfaces in hyperspaces, Proc. of the Academy of Arts and Sciences, 52 (1916), pp. 267-368. JFM46.1133.02
  15. [15] L. Rodriguez - R.A. Tribuzy, Reduction of codimension of 1-regular immersions, preprint. Zbl0524.53038
  16. [16] L. Rodriguez - I. V. GUADALUPE, Normal curvature of surfaces in space forms, Pacific J. of Math, 106 n. 1 (1983). Zbl0515.53044MR694674
  17. [17] M. Spivak, A comprehensive introduction to differential geometry, vol. 4, Publish or Perish, Inc. (1975). Zbl0306.53002
  18. [18] Y.C. Wong, Contributions to the theory of surfaces in 4-space of constant curvature, Trans. Amer. Math. Soc., 59 (1946), pp. 346-366. Zbl0060.38605MR16231

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