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HYPERSURFACES IN ${\mathbb C}$P2 AND ${\mathbb C}$H2 WITH TWO DISTINCT PRINCIPAL CURVATURES

Part of:Global differential geometryGeneral theory in ordinary differential equations

Published online by Cambridge University Press:  21 July 2015

THOMAS A. IVEY and
PATRICK J. RYAN
THOMAS A. IVEY
Affiliation:
Department of Mathematics, College of Charleston, 66 George St., Charleston, SC, USA e-mail: IveyT@cofc.edu
PATRICK J. RYAN
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada e-mail: ryanpj@mcmaster.ca
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Abstract

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It is known that hypersurfaces in ${\mathbb C}$Pn or ${\mathbb C}$Hn for which the number g of distinct principal curvatures satisfies g ≤ 2, must belong to a standard list of Hopf hypersurfaces with constant principal curvatures, provided that n ≥ 3. In this paper, we construct a two-parameter family of non-Hopf hypersurfaces in ${\mathbb C}$P2 and ${\mathbb C}$H2 with g=2 and show that every non-Hopf hypersurface with g=2 is locally of this form.

MSC classification

Primary:53C40: Global submanifolds
Secondary:34A99: None of the above, but in this section

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 1 , January 2016, pp. 137 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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