Characterization of totally umbilic hypersurfaces in a space form by circles
Toshiaki Adachi; Sadahiro Maeda
Czechoslovak Mathematical Journal (2005)
- Volume: 55, Issue: 1, page 203-207
- ISSN: 0011-4642
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topAdachi, Toshiaki, and Maeda, Sadahiro. "Characterization of totally umbilic hypersurfaces in a space form by circles." Czechoslovak Mathematical Journal 55.1 (2005): 203-207. <http://eudml.org/doc/30938>.
@article{Adachi2005,
abstract = {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.},
author = {Adachi, Toshiaki, Maeda, Sadahiro},
journal = {Czechoslovak Mathematical Journal},
keywords = {totally umbilic hypersurfaces; circles; space forms; totally umbilic hypersurfaces; circles; space forms},
language = {eng},
number = {1},
pages = {203-207},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterization of totally umbilic hypersurfaces in a space form by circles},
url = {http://eudml.org/doc/30938},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Adachi, Toshiaki
AU - Maeda, Sadahiro
TI - Characterization of totally umbilic hypersurfaces in a space form by circles
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 203
EP - 207
AB - 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.
LA - eng
KW - totally umbilic hypersurfaces; circles; space forms; totally umbilic hypersurfaces; circles; space forms
UR - http://eudml.org/doc/30938
ER -
References
top- 10.4153/CMB-2000-011-3, Canadian Math. Bull. 43 (2000), 74–78. (2000) MR1749951DOI10.4153/CMB-2000-011-3
- The homogeneity of isoparametric hypersurfaces with six principal curvatures, Preprint Titech-Math. Vol. 80, 1998. (1998)
- Open problems in geometry. Part I, Proc. Sympos. Pure Math. 54 (1993), 1–28. (1993) MR1216573
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