Asian Journal of Mathematics

Volume 9 (2005)

Number 1

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

Pages: 65 – 78

DOI: https://dx.doi.org/10.4310/AJM.2005.v9.n1.a6

Authors

Tsasa Lusala

Mike Scherfner

Luiz Amancio M. Souse, Jr.

Abstract

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