Abstract
We consider minimal closed hypersurfaces M 4 � S 5 (1) with constant scalar curva- ture. We prove that, if M 4 is additionally a Willmore hypersurface, then it is isoparametric. This gives a positive answer to the question made by Chern about the pinching of the scalar curvature for closed minimal Willmore hypersurfaces in dimension 4.
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