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Complete hypersurfaces in cylinders

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  09 April 2009

Thomas Hasanis
Thomas Hasanis
Affiliation:
Department of Mathematics, University of Ioannina 45110, Ioannina, Greece
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Abstract

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We consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.

Keywords

complete hypersurfacebounded sectional curvaturescalar curvature.

MSC classification

Secondary: 53C40: Global submanifolds 53B20: Local Riemannian geometry
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 313 - 318
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Hasanis, Th. and Koutroufiotis, D., ‘Immersions of Riemannian manifolds into cylinders’, Arch. Math. 40 (1983), 82–85.CrossRefGoogle Scholar
[2]Leung, P.-F., ‘Complete hypersurfaces on non-positive Ricci curvature’, Bull. Austral. Math. Soc. 27 (1983), 215–219.CrossRefGoogle Scholar
[3]Omori, H., ‘Isometric immersions of Riemannian manifolds’, J. Math. Soc. Japan 19 (1967), 205–214.CrossRefGoogle Scholar