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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.

Closed Minimal Willimore Hypersurfaces of <b>S</b><sup>5</sup>(1) with Constant Scalar Curvature