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Conformally flat hypersurfaces with constant Gauss-Kronecker curvature

Published online by Cambridge University Press:  17 April 2009

Filip Defever
Filip Defever
Affiliation:
Departement Wiskunde, KU Leuven, Celestijnenlaan 200 B, 3001 Heverlee (Leuven), Belgium, e-mail: Filip.Defever@wis.kuleuvan.ac.be
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Abstract

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We consider 3-dimensional conformally flat hypersurfaces of E4 with constant Gauss-Kronecker curvature. We prove that those with three different principal curvatures must necessarily have zero Gauss-Kronecker curvature.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 207 - 216
Copyright
Copyright © Australian Mathematical Society 2000

References

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