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A characterization of quadrics by the principal curvature functions

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Abstract.

We consider the difference tensor field of the Levi-Civita connections of the first and third fundamental form for non-degenerate hypersurface immersions in space forms. Within this framework, we characterize quadrics in terms of their principal curvature functions.

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Authors and Affiliations

  1. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001, Leuven - Heverlee, Belgium

    F. Dillen & G. Verbouwe

  2. Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    T. Lusala & M. Scherfner

Authors
  1. F. Dillen
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  2. T. Lusala
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  3. M. Scherfner
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  4. G. Verbouwe
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Corresponding authors

Correspondence to F. Dillen or T. Lusala.

Additional information

Received: 17 May 2002; revised manuscript accepted: 5 August 2002

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Dillen, F., Lusala, T., Scherfner, M. et al. A characterization of quadrics by the principal curvature functions. Arch. Math. 81, 342–347 (2003). https://doi.org/10.1007/s00013-003-4735-8

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  • DOI: https://doi.org/10.1007/s00013-003-4735-8

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