# Willmore spheres in quaternionic projective space

Source: [Willmore spheres in quaternionic projective space](<https://www.sota2.com/research/paper/68fa4d241e209131ce9520d9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:09:32.077Z

Authors: K. Leschke

Published: 2002-09-26T13:40:57.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0209359>)

[PDF](<https://arxiv.org/pdf/math/0209359.pdf>)