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Complete minimal hypersurfaces in with zero Gauss–Kronecker curvature

Published online by Cambridge University Press:  12 February 2007

TH. HASANIS ,
A. SAVAS–HALILAJ  and
TH. VLACHOS
TH. HASANIS
Affiliation:
Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece. e-mail: thasanis@cc.uoi.gr, me00499@cc.uoi.gr, tvlachos@cc.uoi.gr
A. SAVAS–HALILAJ
Affiliation:
Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece. e-mail: thasanis@cc.uoi.gr, me00499@cc.uoi.gr, tvlachos@cc.uoi.gr
TH. VLACHOS
Affiliation:
Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece. e-mail: thasanis@cc.uoi.gr, me00499@cc.uoi.gr, tvlachos@cc.uoi.gr
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Abstract

We investigate the structure of 3-dimensional complete minimal hypersurfaces in the unit sphere with Gauss–Kronecker curvature identically zero.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 125 - 132
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] Almeida, S. C. de and Brito, F.G.B.. Minimal hypersurfaces of with constant Gauss–Kronecker curvature. Math. Z. 195 (1987), 99–107.Google Scholar
[2] Asperti, A. C.. Immersions of surfaces into 4-dimensional spaces with nonzero normal curvature. Ann. Mat. Pura Appl. 125 (1980), 313–328.CrossRefGoogle Scholar
[3] Bryant, R.. Conformal and minimal immersions of compact surfaces into the 4-sphere. J. Differential Geom. 17 (1982), 455–473.CrossRefGoogle Scholar
[4] Cheng, S. Y. and Yau, S. T.. Maximal space-like hypersurfaces in the Lorentz–Minkowski spaces. Ann. of Math. (2) 104 (1976), 407–419.CrossRefGoogle Scholar
[5] Dajczer, M. and Gromoll, D.. Gauss parametrizations and rigidity aspects of submanifolds. J. Differential Geom. 22 (1985), 1–12.CrossRefGoogle Scholar
[6] Palais, R.. A global formulation of the Lie theory of transformation groups. Mem. Amer. Math. Soc. 22 (1957).Google Scholar
[7] Ramanathan, J.. Minimal hypersurfaces of with vanishing Gauss–Kronecker curvature. Math. Z. 205 (1990), 645–658.CrossRefGoogle Scholar
[8] Tribuzy, R. and Guadalupe, I. V.. Minimal immersions of surfaces into 4-dimensional space forms. Rend. Sem. Math. Univ. Padova 73 (1985), 1–13.Google Scholar