Journal of the Australian Mathematical Society (Series A)
- Journal of the Australian Mathematical Society (Series A) / Volume 46 / Issue 02 / April 1989, pp 313-318
- Copyright © Australian Mathematical Society 1989
- DOI: http://dx.doi.org/10.1017/S1446788700030792 (About DOI), Published online: 09 April 2009
Research Article
Complete hypersurfaces in cylinders
Thomas Hasanisa1
a1 Department of Mathematics, University of Ioannina 45110, Ioannina, Greece
Abstract
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.
(Received March 25 1987)
(Revised February 12 1988)
1980 Mathematics subject classification (Amer. Math. Soc.)
- primary 53 C 40;
- secondary 53 B 20
Keywords and phrases
- complete hypersurface;
- bounded sectional curvature;
- scalar curvature.
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