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

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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

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  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

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