Hipersuperfícies fechadas de S4 com curvatura constante de Gauss-Kronecker - Almeida, Sebastião Carneiro de (1997)
In this paper as in ([AB1], [AB2]) we are concerned with the study of closed hypersurfaces in the unit 4-sphere with two constant symmetric curvature functions. If one of the assumptions refers to the scalar curvature of the hypersurfaces M as non-negative constant then M must be isoparametric. There is a similar result for hypersurfaces with constant mean curvature and constant Gauss-Kronecker curvature.