Minimal immersions of surfaces into 4-dimensional space forms
Tribuzy, Renato de Azevedo ; Valle Guadalupe, Irwen
Rendiconti del Seminario Matematico della Università di Padova, Tome 74 (1985), p. 1-13 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1985-01-01
@article{RSMUP_1985__73__1_0,
     author = {Tribuzy, Renato de Azevedo and Valle Guadalupe, Irwen},
     title = {Minimal immersions of surfaces into $4$-dimensional space forms},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {74},
     year = {1985},
     pages = {1-13},
     mrnumber = {799891},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1985__73__1_0}
}

Tribuzy, Renato de Azevedo; Valle Guadalupe, Irwen. Minimal immersions of surfaces into $4$-dimensional space forms. Rendiconti del Seminario Matematico della Università di Padova, Tome 74 (1985) pp. 1-13. http://gdmltest.u-ga.fr/item/RSMUP_1985__73__1_0/

[1] L. Ahlfors - L. Sario, Riemann surfaces, Princeton University Press, Princeton, 1960. | MR 114911 | Zbl 0196.33801

[2] A.C. Asperti, Immersions of surfaces into 4-dimensional spaces with nonzero normal curvature, Ann. Mat. Pura Appl., 125 (1980), pp. 313-328. | MR 605213 | Zbl 0453.53045

[3] L.R. Bryant, Every compact Riemann surface may be immersed conformally and minimally into S4, preprint.

[4] E. Calabi, Minimal immersions of surfaces in euclidean spheres, J. Diff. Geometry, 1 (1967), pp. 111-125. | MR 233294 | Zbl 0171.20504

[5] M. Do Carmo - N. Wallach, Representation of compact groups and minimal immersions into spheres, J. Diff. Geometry, 4 (1970), pp. 91-104. | MR 266104 | Zbl 0197.18301

[6] B.Y. Chen, Geometry of submanifolds, New York, M. Dekker (1973). | MR 353212 | Zbl 0262.53036

[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. | MR 278205 | Zbl 0212.26402

[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. | MR 362151 | Zbl 0217.47601

[9] S.S. Chern - R. Osserman, Remarks on the Riemannian metric of a minimal submanifold, preprint.

[10] T. Itoh, Minimal surfaces in 4-dimensional Riemannian manifolds of constant curvature, Kodai Math. Sem. Rep., 23 (1971), pp. 415-458. | MR 317248 | Zbl 0249.53045

[11] H.B. Lawsonjr., Complete minimal surfaces in S3, Ann. of Math., 92 (1970), pp. 335-374. | Zbl 0205.52001

[12] H.B. Lawsonjr., Some intrinsic characterizations of minimal surfaces, J. d'Analyse Mathematique, 24 (1971), pp. 152-161. | MR 284922 | Zbl 0251.53003

[13] J.A. Little, On singularities of submanifolds of a higher dimensional Euclidean space, Ann. Mat. Pura Appl., 83 (1969), pp. 261-335. | MR 271970 | Zbl 0187.18903

[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. | JFM 46.1133.02

[15] L. Rodriguez - R.A. Tribuzy, Reduction of codimension of 1-regular immersions, preprint.

[16] L. Rodriguez - I. V. GUADALUPE, Normal curvature of surfaces in space forms, Pacific J. of Math, 106 n. 1 (1983). | MR 694674 | Zbl 0515.53044

[17] M. Spivak, A comprehensive introduction to differential geometry, vol. 4, Publish or Perish, Inc. (1975). | Zbl 0306.53002

[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. | MR 16231 | Zbl 0060.38605