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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Complete minimal hypersurfaces in the hyperbolic space $ \mathbb{H}^{4}$ with vanishing Gauss-Kronecker curvature


Authors: T. Hasanis, A. Savas-Halilaj and T. Vlachos
Journal: Trans. Amer. Math. Soc. 359 (2007), 2799-2818
MSC (2000): Primary 53C40; Secondary 53C42, 53C50
Published electronically: January 26, 2007
MathSciNet review: 2286057
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Abstract: We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $ \mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, a nowhere vanishing second fundamental form and a scalar curvature bounded from below.


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Additional Information

T. Hasanis
Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Email: thasanis@cc.uoi.gr

A. Savas-Halilaj
Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Email: me00499@cc.uoi.gr

T. Vlachos
Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
Email: tvlachos@cc.uoi.gr

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04231-6
PII: S 0002-9947(07)04231-6
Keywords: Hyperbolic space, minimal hypersurface, second fundamental form, Gauss-Kronecker curvature, stationary surface.
Received by editor(s): April 27, 2005
Published electronically: January 26, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.