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Willmore spheres in quaternionic projective space

Name: Willmore spheres in quaternionic projective space
Creator: Leschke, K.
Keywords: Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), FOS: Mathematics, 53Axx, 53Cxx, 30Fxx, 0101 mathematics, 01 natural sciences, Algebraic Geometry (math.AG)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2002Embargo end date: 01 Jan 2002Publisher:arXiv

Authors: Leschke, K.;

doi: 10.48550/arxiv.math/0209359

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

Willmore spheres in quaternionic projective space

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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.

23 pages, v2: improved presentation, qualified references added

Keywords

Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), FOS: Mathematics, 53Axx, 53Cxx, 30Fxx, Algebraic Geometry (math.AG)

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