Complete minimal hypersurfaces in the hyperbolic space $\mathbb {H}^{4}$ with vanishing Gauss-Kronecker curvature
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- by T. Hasanis, A. Savas-Halilaj and T. Vlachos PDF
- Trans. Amer. Math. Soc. 359 (2007), 2799-2818 Request permission
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.References
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Additional Information
- T. Hasanis
- Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- MR Author ID: 82090
- Email: thasanis@cc.uoi.gr
- A. Savas-Halilaj
- Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- MR Author ID: 045365
- Email: me00499@cc.uoi.gr
- T. Vlachos
- Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- MR Author ID: 291296
- Email: tvlachos@cc.uoi.gr
- Received by editor(s): April 27, 2005
- Published electronically: January 26, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2799-2818
- MSC (2000): Primary 53C40; Secondary 53C42, 53C50
- DOI: https://doi.org/10.1090/S0002-9947-07-04231-6
- MathSciNet review: 2286057