| Title:
|
Characterization of totally umbilic hypersurfaces in a space form by circles (English) |
| Author:
|
Adachi, Toshiaki |
| Author:
|
Maeda, Sadahiro |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
203-207 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda. (English) |
| Keyword:
|
totally umbilic hypersurfaces |
| Keyword:
|
circles |
| Keyword:
|
space forms |
| MSC:
|
53B25 |
| MSC:
|
53C40 |
| idZBL:
|
Zbl 1081.53020 |
| idMR:
|
MR2121667 |
| . |
| Date available:
|
2009-09-24T11:22:13Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127970 |
| . |
| Reference:
|
[1] M. Kimura and S. Maeda: Geometric meaning of isoparametric hypersurfaces in a real space form.Canadian Math. Bull. 43 (2000), 74–78. MR 1749951, 10.4153/CMB-2000-011-3 |
| Reference:
|
[2] R. Miyaoka: The homogeneity of isoparametric hypersurfaces with six principal curvatures.Preprint Titech-Math. Vol. 80, 1998. |
| Reference:
|
[3] S. T. Yau: Open problems in geometry. Part I.Proc. Sympos. Pure Math. 54 (1993), 1–28. MR 1216573 |
| . |
