Willmore spheres in quaternionic projective space

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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.
23 pages, v2: improved presentation, qualified references added

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Differential Geometry, Algebraic Geometry, 53Axx, 53Cxx, 30Fxx

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http://salesiana.dossiersoluciones.com/handle/123456789/99814

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209359
 http://arxiv.org/abs/math/0209359

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arXiv