The geometry of closed hypersurfaces

Sebastião de Almeida; Fabiano Brito

Séminaire de théorie spectrale et géométrie (1987-1988)

  • Volume: 6, page 109-116
  • ISSN: 1624-5458

How to cite

top

de Almeida, Sebastião, and Brito, Fabiano. "The geometry of closed hypersurfaces." Séminaire de théorie spectrale et géométrie 6 (1987-1988): 109-116. <http://eudml.org/doc/114274>.

@article{deAlmeida1987-1988,
author = {de Almeida, Sebastião, Brito, Fabiano},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {minimal hypersurfaces; isoparametric hypersurfaces; th mean curvature; 4-dimensional space forms},
language = {eng},
pages = {109-116},
publisher = {Institut Fourier},
title = {The geometry of closed hypersurfaces},
url = {http://eudml.org/doc/114274},
volume = {6},
year = {1987-1988},
}

TY - JOUR
AU - de Almeida, Sebastião
AU - Brito, Fabiano
TI - The geometry of closed hypersurfaces
JO - Séminaire de théorie spectrale et géométrie
PY - 1987-1988
PB - Institut Fourier
VL - 6
SP - 109
EP - 116
LA - eng
KW - minimal hypersurfaces; isoparametric hypersurfaces; th mean curvature; 4-dimensional space forms
UR - http://eudml.org/doc/114274
ER -

References

top
  1. [1] ALEKSANDROV A.D. - Uniqueness theorems for surfaces in the large, Vestnik Leningrad Univ. Math., 13 ( 1958), 5-8. Zbl0119.16603MR102114
  2. [2] ALMEIDA S.C. - Minimal hypersurfaces of S4 with non-zero Gauss-Kronecker curvature, Bol. Soc. Bras. Math. , 14 n° 2 ( 1983), 137-146. Zbl0569.53025MR756907
  3. [3] ALMEIDA S.C. - Minimal hypersurfaces of a positive scalar curvature manifold, Math. Z., 190 ( 1975), 73-82. Zbl0549.53059MR793350
  4. [4] ALMEIDA S.C. and BRITO F. G. B. - Minimal hypersurfaces of S4 with constant Gauss-Kronecker curvature, Math. Z., 195 ( 1987), 99-107. Zbl0602.53040MR888131
  5. [5] BRITO F.G. - Uma restriçāo para a curvatura escalar de hipersuperficies de S4 com curvatura media constante, IME-USP (Livre Docencia). 
  6. [6] CHERN S.S., DO CARMO M., KOBAYASHI S. - Minimal submanifolds of the sphere with second fundamental form of constant length, Functional analysis and related fields ed. F. Browder. Berlin Heidelberg New York, Springer, 1970. Zbl0216.44001
  7. [7] GUADALUPE I.V., TRIBUZY R. - Minimal immersions of surfaces into space forms, Rendiconti del Seminario Mathematico delia Universita di Padova, 73 ( 1985), 1-13. Zbl0573.53036MR799891
  8. [8] HSIANG W.Y., TENG Z.H., YU W.C. - New examples of constant mean curvature immersions of (2k - 1) spheres into Euclidean 2k-space, Ann. of Math., 117 ( 1983), 609-625. Zbl0522.53052MR701257
  9. [9] HSIUNG C.C. - Some integral formulas for closed hypersurfaces, Math. Scand., 2 ( 1954), 286-294. Zbl0057.14603MR68236
  10. [10] LAWSON H.B. JR., - Local rigidity theorems for minimal hypersurfaces, Ann. of Math, 89 ( 1969), 187-197. Zbl0174.24901MR238229
  11. [11] LAWSON H.B. JR., - Complete minimal surfaces in S3, Ann. of Math., 92 (2) ( 1970), 335-374. Zbl0205.52001MR270280
  12. [12] LAWSON H.B. JR., - The unknottedness of minimal embeddings, Invent. Math., 11 ( 1970), 183-187. Zbl0205.52002MR287447
  13. [13] MEEKS W., SIMON L., YAU S.T.. - Embedded minimal surfaces, exotic spheres, and manifolds of positive Ricci curvature, Ann. of Math., 116 ( 1982), 621-659. Zbl0521.53007MR678484
  14. [14] NOMIZU K. - Elie Cartan's work on isoparametric families of hypersurfaces, Proceedings of Symposia in Pure Mathematics, 27, 1975. Zbl0318.53052
  15. [15] PENG C.K., TERNG C. L. - The scalar curvature of minimal hypersurfaces in spheres. Mat Ann., 266 ( 1983), 105-113. Zbl0508.53060MR722930
  16. [16] RAMANATHAN J. - Minimal hypersurfaces in S4 with vanishing Gauss-Kronecker curvature, To appear. Zbl0694.53054MR1082881
  17. [17] ROS A. - Compact hypersurfaces with constant scalar curvature and a congruence theorem, J. Differential Geometry , 27 ( 1988), 215-220. Zbl0638.53051MR925120
  18. [18] WENTE H.C. - Counterexample to a conjecture of H. Hopf, Pacific J. Math., 121 ( 1986), 193-243. Zbl0586.53003MR815044

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.