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Willmore spheres in quaternionic projective space

K. Leschke
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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.

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K. Leschke. 2005-10-28. Willmore spheres in quaternionic projective space. https://arxiv.org/abs/math/0209359

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