Characterization of totally umbilic hypersurfaces in a space form by circles
Toshiaki Adachi, Sadahiro Maeda (2005)
Czechoslovak Mathematical Journal
Similarity:
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.