# Sequences of harmonic maps in the 3-sphere

@article{Dioos2014SequencesOH, title={Sequences of harmonic maps in the 3-sphere}, author={Bart Dioos and J. Veken and L. Vrancken}, journal={Mathematische Nachrichten}, year={2014}, volume={288}, pages={2001-2015} }

We define two transforms of 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 harmonic maps into the 3-sphere, H-surfaces in Euclidean 3-space and almost complex surfaces in the nearly Kahler manifold . As a consequence we can construct sequences of H-surfaces and almost complex surfaces.

#### 10 Citations

Non-conformal harmonic maps into the 3-sphere

- Mathematics
- 2015

We present two transforms of non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct from one non-conformal harmonic map a sequence of non-conformal… Expand

The Bonnet problem for harmonic maps to the three-sphere

- Mathematics
- 2019

Abstract In previous work [15] the authors defined transforms for non-conformal harmonic maps from a Riemann surface into the 3-sphere. An observation from that study was that two invariants, a real… Expand

Transforms for Non-conformal Harmonic Surfaces in $$\varvec{R^3}$$R3

- Mathematics
- 2017

For a non-conformal harmonic surface in $$R^3$$R3, we give transforms to get holomorphic maps to the 2-sphere, which is a generalization of the classical fact that the Gauss map of a minimal surface… Expand

Rigidity of the almost complex surfaces in the nearly Kähler S3×S3

- Mathematics
- 2016

Abstract In this paper we first show that the well-known nearly Kahler manifold S 3 × S 3 is neither locally symmetric nor Chern flat. Then, by studying the rigidity of compact almost complex… Expand

A representation formula for non-conformal harmonic surfaces in $R^3$

- Physics, Mathematics
- 2017

We discuss non-conformal harmonic surfaces in $R^3$ with prescribed ($\pm$)transforms, and we get a representation formula for non-conformal harmonic surfaces in $R^3$.

Lagrangian submanifolds in the 6-dimensional nearly Kähler manifolds with parallel second fundamental form

- Mathematics
- 2016

Abstract In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kahler S 3 × S 3 with parallel second fundamental form. We first prove that every Lagrangian submanifold with… Expand

A Representation Formula for Non-conformal Harmonic Surfaces in $$\varvec{R}^{\mathbf{3}}$$R3

- Mathematics
- 2019

We discuss non-conformal harmonic surfaces in $$R^3$$R3 with prescribed (±)transforms, and we get a representation formula for non-conformal harmonic surfaces in $$R^3$$R3.

On some hypersurfaces of the homogeneous nearly Kähler S3×S3

- Mathematics
- 2018

In this paper, we study hypersurfaces of the homogeneous nearly Kahler manifold S3×S3 with typical properties. We first show that in the NK S3×S3 there exist neither totally umbilical hypersurfaces… Expand

Transforms for minimal surfaces in 5-dimensional space forms

- Mathematics
- 2017

For a minimal surface in a 5-dimensional space form, we give transforms to get another minimal surface in another 5-or 4-dimensional space form.

Isotropic Lagrangian submanifolds in the homogeneous nearly Kähler S3 × S3

- Mathematics
- 2016

We show that isotropic Lagrangian submanifolds in a 6-dimensional strict nearly Kähler manifold are totally geodesic. Moreover, under some weaker conditions, a complete classification of the… Expand

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