| Title:
|
Variétés pseudo-ombilicales de codimension 2 et de courbure moyenne constante dans un espace elliptique à $n+2$ dimensions et généralisations (French) |
| Title:
|
Pseudo-umbilical manifolds of codimension 2 and of constant mean curvature in an $(n+2)$-dimensional elliptic space and generalisations (English) |
| Author:
|
Vanhecke, Lieven |
| Language:
|
French |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
23 |
| Issue:
|
3 |
| Year:
|
1973 |
| Pages:
|
404-412 |
| . |
| Category:
|
math |
| . |
| MSC:
|
53A35 |
| idZBL:
|
Zbl 0265.53019 |
| idMR:
|
MR0334012 |
| DOI:
|
10.21136/CMJ.1973.101182 |
| . |
| Date available:
|
2008-06-09T14:02:50Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101182 |
| . |
| Reference:
|
[1] E. Cartan: La géométrie des espaces de Riemann.Mém. Sc. Math., Fasc. IX, Gauthier-Villars, Paris (1925). |
| Reference:
|
[2] B. Y. Chen: On an inequality of mean curvatures of higher degree.Bull. Am. Math. Soc., 77 (1971). Zbl 0206.24103, MR 0267491 |
| Reference:
|
[3] B. Y. Chen: Minimal hypersurfaces in an $m$-sphere.Proc. Am. Soc., 29 (1971). Zbl 0203.53803, MR 0285999 |
| Reference:
|
[4] S. S. Chern N. H. Kuiper: Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space.Ann. of Math., vol. 56, 3 (1952). MR 0050962 |
| Reference:
|
[5] T. Ôtsuki: Minimal hypersurfaces in a Riemannian manifold of constant curvature.Am. J. of Math., 192 (1970). MR 0264565 |
| Reference:
|
[6] R. Rosea F. Borel: Sur les autotransformations infinitésimales équivalentes des variétés minimales à deux dimensions d'un espace elliptique $n$-dimensionnel.C.R. Acad. Sc. Paris, t. 268, p. 399-401 (1969), série A. |
| Reference:
|
[7] R. Rosea L. Vanhecke L. Verstraelen: Triade rectangulaire de variétés bidimensionnelles dont l'une est minimale et les deux autres pseudo-ombilicales et de $m$-index $V^2 = 1$, immergées dans un espace elliptique à quatre dimensions.Bull. Soc. Math. Belg. XXIV, 3 (1972). |
| Reference:
|
[8] R. Takagi: Homogeneous hypersurfaces in a sphere with the type number 2.Tôhoku Math. Journ., 23 (1971). Zbl 0213.48702, MR 0290311, 10.2748/tmj/1178242686 |
| Reference:
|
[9] Y. С. Wong: A note on complementary subspaces in a Riemannian space.Bull. Am. Soc., 49 (1943). Zbl 0060.38603, MR 0008188 |
| Reference:
|
[10] K. Yano, B. Y. Chen: Minimal submanifolds of a higher dimensional sphere.Tensor, 22(1971). Zbl 0218.53073, MR 0287495 |
| . |
