Isoparametric Hypersurfaces in Sn+1: The Chern Conjecture

BasicsThe ChernConjectureBasicsTheConjectureResultsGeneralizationsSummaryOutlookWe are concerned with hypersurfaces, i. e. n-dimensionalsubmanifolds in (n + 1)-dimensional Riemannian manifolds.The curvature of a hypersurface M in the ambient manifold isdescribed by the second fundamental form h (or the associatedshape operator A). The eigenvalues of h are the principalcurvature functions λ i , i = 1...n.