IJPAM: Volume 39, No. 1 (2007)

A NOTE ON MINIMAL HYPERSURFACES
OF THE UNIT SPHERE

Sharief Deshmukh$^1$, Falleh R. Al-Solamy$^2$
$^{1}$Department of Mathematics
College of Science
King Saud University
P.O. Box 2455, Riyadh, 11451, KINGDOM OF SAUDI ARABIA
e-mail: shariefd@ksu.edu.sa
$^{2}$Department of Mathematics
King Abdul Aziz University
P.O. Box 80015, Jeddah, 21589, KINGDOM OF SAUDI ARABIA
e-mail: falleh@hotmail.com


Abstract.In this note, we show that for compact and connected minimal hypersurfaces of constant scalar curvature in the unit sphere $S^{n+1}(1)$ the set of values that the square of the length of the shape operator can assume is discrete.

Received: April 21, 2007

AMS Subject Classification: 53C20, 53C40

Key Words and Phrases: hypersurfaces, minimal hypersurfaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 1