Willmore spheres in quaternionic projective space

TL;DR

This paper generalizes the concept of Willmore spheres to quaternionic projective space, showing they have integer energy and are characterized by complex holomorphic data, extending Bryant's classical results.

Contribution

It introduces a Baecklund transformation for Willmore curves in quaternionic projective space, generalizing Bryant's results to higher-dimensional settings.

Findings

Willmore spheres in quaternionic projective space have integer Willmore energy.

They are characterized by complex holomorphic data.

The paper extends classical results from 3-space to quaternionic projective space.

Abstract

The Willmore energy for Frenet curves in quaternionic projective space is the generalization of the Willmore functional for immersions into the 4-sphere. Critical points of the Willmore energy are called Willmore curves in quaternionic projective space. Using a Baecklund transformation on Willmore curves, we generalize Bryant's result on Willmore spheres in 3--space: a Willmore sphere in quaternionic projective space has integer Willmore energy, and is given by complex holomorphic data.