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Characterization of totally umbilic hypersurfaces in a space form by circles

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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.

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References

  1. M. Kimura and S. Maeda: Geometric meaning of isoparametric hypersurfaces in a real space form. Canadian Math. Bull. 43 (2000), 74–78.

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Authors and Affiliations

  1. Dept. of Mathematics, Nagoya Institute of Technology, 466-8555, Gokiso, Nagoya, Japan

    Toshiaki Adachi

  2. Dept. of Mathematics, Shimane University, 690-8504, Matsue, Shimane, Japan

    Sadahiro Maeda

Authors
  1. Toshiaki Adachi
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  2. Sadahiro Maeda
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Additional information

The first author was partially supported by Grant-in-Aid for Scientific Research (C) No. 14540075, Ministry of Education, Science, Sports and Culture. The second author was partially supported by Grant-in-Aid for Scientific Research (C) No. 14540080, Ministry of Education, Science, Sports and Culture.

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Adachi, T., Maeda, S. Characterization of totally umbilic hypersurfaces in a space form by circles. Czech Math J 55, 203–207 (2005). https://doi.org/10.1007/s10587-005-0015-z

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  • DOI: https://doi.org/10.1007/s10587-005-0015-z

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