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Divisibility of the Second Fundamental Form of Hypersurfaces of Space Forms

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Abstract.

We classify the hypersurfaces of space forms for which the cubic form is divisible by the metric (g|C). In other words, when does the symmetric traceless part of the cubic form vanish, where the trace is taken with respect to the first fundamental form?

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Authors and Affiliations

  1. Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, Box 2400, B-3001, Leuven, Belgium

    Franki Dillen & Gerd Verbouwe

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  1. Franki Dillen
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  2. Gerd Verbouwe
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Correspondence to Franki Dillen.

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Dedicated to Udo Simon on the occasion of his 70th birthday

This research was supported by Research Grant G.0432.07 of the Research Foundation-Flanders (FWO).

Received: April 22, 2008. Accepted: June 1, 2008.

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Dillen, F., Verbouwe, G. Divisibility of the Second Fundamental Form of Hypersurfaces of Space Forms. Result. Math. 52, 247–260 (2008). https://doi.org/10.1007/s00025-008-0308-2

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  • DOI: https://doi.org/10.1007/s00025-008-0308-2

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