Equivariant harmonic cylinders

Abstract

We prove that a primitive harmonic map is equivariant if and only if it admits a holomorphic potential of degree one. We investigate when the equivariant harmonic map is periodic, and as an application discuss constant mean curvature cylinders with screw motion symmetries.

References in corpus (3)

• Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms
• Harmonic maps in unfashionable geometries
• Bäcklund Transformations and Loop Group Actions

Cited by in corpus (10)

• Willmore surfaces in spheres via loop groups $I$: generic cases and some examples
• On the moduli of constant mean curvature cylinders of finite type in the 3-sphere
• On the Björling problem for Willmore surfaces
• Minimal Lagrangian surfaces in $\mathbb{C}{P}^2$ via the loop group method Part I: the contractible case
• Explicit expressions for the Iwasawa factors, the metric and the monodromy matrices for minimal Lagrangian surfaces in $\mathbb{C}{P}^2$
• Classification of Homogeneous Willmore Surfaces in $S^N$
• Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-space
• Topologically embedded pseudospherical cylinders
• Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group
• The space of equivariant harmonic tori in the 3-sphere