S¹-Equivariant CMC Surfaces in the Berger Sphere and the Corresponding Lagrangians

Keiichi Kikuchi

Department of Mathematics, Tokai University, Tokyo, Japan.

DOI: 10.4236/apm.2013.32037                

Abstract

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.

Keywords

S¹-Equivariant CMC Surfaces; Conservation Laws

Conflicts of Interest

The authors declare no conflicts of interest.

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