Willmore spheres in quaternionic projective space

Details Willmore spheres in quaternionic projective space Willmore spheres in quaternionic projective space

2002-09-26

arxiv.org/abs/math/0209359v2

Mathematics

Differential Geometry

23 pages, v2: improved presentation, qualified references added

Scientific paper

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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