English

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