A note on the Chern Conjecture in dimension four

Abstract

Let M 4 be a closed immersed minimal hypersurface with constant squared length of the second fundamental form S and constant 3-mean curvature H3 in S 5 . If3 ≤ 1 2 and Gauss-Kronecker curvature KM satisfies KM ≤ 1 (or KM ≤ S 2 144 ), then M 4 is isoparametric.