\(S^1\)-equivariant CMC surfaces in the Berger sphere, the hyperbolic 3-space and the corresponding Hamiltonian systems. (English) Zbl 1286.53067
Summary: The Hamiltonian system corresponding to \(S^1\)-equivariant CMC surfaces in the Berger sphere or the hyperbolic 3-space is constructed. The corresponding Lagrangian is equipped with suitable potential function and the Euler-Lagrange equation is effectively applied to the determination of its potential function.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C43 | Differential geometric aspects of harmonic maps |
| 70H03 | Lagrange’s equations |
