Sequences of harmonic maps in the 3-sphere

TL;DR

This paper introduces two transforms that generate sequences of non-conformal harmonic maps into the 3-sphere, revealing connections with H-surfaces in Euclidean space and almost complex surfaces in a nearly Kähler manifold.

Contribution

It defines new transforms for harmonic maps into S^3 and establishes a correspondence with H-surfaces and almost complex surfaces, enabling sequence construction.

Findings

Constructed sequences of harmonic maps from a single initial map.

Established a correspondence between harmonic maps, H-surfaces, and almost complex surfaces.

Provided a method to generate new geometric surfaces from harmonic maps.

Abstract

We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between non-conformal harmonic maps into the 3-sphere, $H$-surfaces in Euclidean 3-space and almost complex surfaces in the nearly K\"ahler manifold $S^3\times S^3$. As a consequence we can construct sequences of $H$-surfaces and almost complex surfaces.