Willmore spheres in quaternionic projective space
Differential Geometry
2007-05-23 v2 Algebraic Geometry
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.
Cite
@article{arxiv.math/0209359,
title = {Willmore spheres in quaternionic projective space},
author = {K. Leschke},
journal= {arXiv preprint arXiv:math/0209359},
year = {2007}
}
Comments
23 pages, v2: improved presentation, qualified references added