Asian Journal of Mathematics

Volume 9 (2005)

Number 1

Closed Minimal Willimore Hypersurfaces of S5(1) with Constant Scalar Curvature

Pages: 65 – 78



Tsasa Lusala

Mike Scherfner

Luiz Amancio M. Souse, Jr.


We consider minimal closed hypersurfaces M4 subset S5(1) with constant scalar curvature. We prove that, if M4 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.

Published 1 January 2005