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The periodic s1-equivariant hypersurfaces of constant mean curvature can be obtained by using the Lagrangians with suitable potential functions in the Berger spheres. In the corresponding Hamiltonian system, the conservation law is effectively applied to the construction of periodic s1-equivariant surfaces of arbitrary positive constant mean curvature.

advances in pure mathematics

&amp;lt;i&amp;gt;S&amp;lt;/i&amp;gt;&amp;lt;sup&amp;gt;1&amp;lt;/sup&amp;gt;-Equivariant CMC Surfaces in the Berger Sphere and the Corresponding Lagrangians