Equivariant primitive harmonic maps into $k-$symmetric spaces, with applications to Willmore surfaces

TL;DR

This paper develops methods for constructing equivariant primitive harmonic maps into k-symmetric spaces and applies these to generate new examples of Willmore surfaces, including equivariant Willmore Moebius strips in S^3.

Contribution

It introduces a novel approach for constructing equivariant primitive harmonic maps into k-symmetric spaces with applications to Willmore surfaces.

Findings

Constructed new equivariant primitive harmonic maps into k-symmetric spaces.

Generated examples of S^1-equivariant Willmore Moebius strips in S^3.

Extended Lawson minimal Klein Bottles to new Willmore surface configurations.

Abstract

In this note we discuss the construction of equivariant primitive harmonic maps into $k-$symmetric spaces and give many applications to the construction of Willmore surfaces. In particular, examples of $S^1-$equivariant Willmore Moebius strips in $S^3$ are obtained as generalizations of the Lawson minimal Klein Bottles in $S^3$.