Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1989 - Volume 46, Issue 02  

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.