Abstract:Let M 4 be a closed minimal hypersurface in S 5 with constant nonnegative scalar curvature. Denote by f 3 the sum of the cubes of all principal curvatures, by g the number of distinct principal curvatures. We prove that, if both f 3 and g are constant, then M 4 is isoparametric. Moreover, We give all possible values for squared length of the second fundamental form of M 4 . This result provides another piece of supporting evidence to the Chern conjecture.
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