Equivariant geometry in EuclideanG-spheres of cohomogeneity two, I

Abstract

The techniques of equivariant geometry are applied to a specific problem in Riemannian geometry, namely the study of constant mean curvature (and minimal) hypersurfaces of the Euclidean sphereS n , subject to the constraint of being invariant with respect to a suitable connected symmetry groupG ⊂ Iso(S n ), dimS n /G=2.