On $G$-invariant minimal hypersurfaces with constant scalar curvature in $S^5$

Commun. Korean Math. Soc. 2002 Vol. 17, No. 2, 261-278 Printed June 1, 2002

Jae-Up So Chonbuk National University

Abstract : Let $G=O(2) \times O(2) \times O(2)$ and let $M^4$ be a closed $G$-invariant minimal hypersurface with constant scalar curvature in $S^5$. If $M^4$ has $2$ distinct principal curvatures at some point, then $S=4$. Moreover, if $S>4$, then $M^4$ does not have simple principal curvatures everywhere.