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.
Keywords : scalar curvature, $G$-invariant minimal hypersurface, square norm
MSC numbers : 53C42
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