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In this paper we introduce the notion of special Weingarten surfaces of minimal type in S 3 . Applying equivariant geometry techniques we construct rotational examples and study the embedness problem for those special surfaces. Mathematics Subject Classification (2000). 53C42, 53C40.

After nearly 50 years of research the Chern conjecture for isoparametric hypersurfaces in spheres is still an unsolved and important problem. Here we give a partial result for CMC hypersurfaces with constant Gauß–Kronecker curvature, mainly using a result given in [3] by Otsuki.